What a gate cannot tell you. 70 gates check structure, provenance, voice and
language. None checks whether an answer is right.manager_signoff printing DONE
has never meant the physics is correct — this page is the part that needs a human.
Why this order. Two compilation answers have already been proven wrong on
this project: an adiabatic-process question recorded as B when the official NTA key says
C, and a rotational item keyed B=70 when the physics gives 140. So items whose
answer came from a published compilation are checked first. Items with no recorded tier come next —
unknown provenance is not verified provenance.
547 PYQ need a human, out of 979 shipped.
Also unverified and not listed item-by-item: 310 worked solutions, 1705 MCQ keys and
480 mock keys. Checkboxes are local to your browser and are not saved.
A hydrogen atom, initially in the ground state is excited by absorbing a photon of wavelength 980$\overset{\circ}{A}$. The radius of the atom in the excited state, in terms of Bohr radius $a_{0}$ will be : (hc = 12500 eV$\overset{
The time period of revolution of electron in its ground state orbit in a hydrogen atom is 1.6 $\times 10^{-16}$ s. The frequency of revolution of the electron in its first excited state (in $s^{-1}$) is :
The energy required to ionise a hydrogen like ion in its ground state is 9 Rydbergs. What is the wavelength of the radiation emitted when the electron in this ion jumps from the second excited state to the ground state ?
Hydrogen ion and singly ionized helium atom are accelerated, from rest, through the same potential difference. The ratio of final speeds of hydrogen and helium ions is close to :
The first member of the Balmer series of hydrogen atom has a wavelength of 6561 Å. The wavelength of the second member of the Balmer series (in nm) is:
A particle of mass 200 MeV/$c^{2}$ collides with a hydrogen atom at rest. Soon after the collision the particle comes to rest, and the atom recoils and goes to its first excited state. The initial kinetic energy of the particle (i
A particular hydrogen like ion emits radiation of frequency 2.92 $\times 10^{15}$ Hz when it makes transition from n = 3 to n = 1. The frequency in Hz of radiation emitted in transition from n = 2 to n = 1 will be :
Imagine that the electron in a hydrogen atom is replaced by a muon ($\mu$). The mass of muon particle is 207 times that of an electron and charge is equal to the charge of an electron. The ionization potential of this hydrogen ato
The wavelength of the photon emitted by a hydrogen atom when an electron makes a transition from n = 2 to n = 1 state is :
Choose the correct option from the following options given below :
The ratio for the speed of the electron in the $3^{rd}$ orbit of $He^{+}$ to the speed of the electron in the $3^{rd}$ orbit of hydrogen atom will be :
Find the ratio of energies of photons produced due to transition of an electron of hydrogen atom from its (i) second permitted energy level to the first level, and (ii) the highest permitted energy level to the first permitted lev
The momentum of an electron revolving in $\mathrm{n}^{\text {th }}$ orbit is given by : (Symbols have their usual meanings)
Given below are two statements : Statement I : In hydrogen atom, the frequency of radiation emitted when an electron jumps from lower energy orbit ($E_{1}$) to higher energy orbit ($E_{2}$), is given as hf = $E_{1} - E_{2}$ Statem
The magnetic moment of an electron (e) revolving in an orbit around nucleus with an orbital angular momentum is given by :
Hydrogen atom from excited state comes to the ground state by emitting a photon of wavelength $\lambda$. The value of principal quantum number '$n$' of the excited state will be : ($\mathrm{R}:$ Rydberg constant)
The radius of electron's second stationary orbit in Bohr's atom is R. The radius of 3rd orbit will be
A photon is emitted in transition from n = 4 to n = 1 level in hydrogen atom. The corresponding wavelength for this transition is (given, h = 4 $\times$ 10$^{-15}$ eVs) :
A light of energy $12.75 ~\mathrm{eV}$ is incident on a hydrogen atom in its ground state. The atom absorbs the radiation and reaches to one of its excited states. The angular momentum of the atom in the excited state is $\frac{x}
The wavelength of the radiation emitted is $\lambda_0$ when an electron jumps from the second excited state to the first excited state of hydrogen atom. If the electron jumps from the third excited state to the second orbit of the
If the binding energy of ground state electron in a hydrogen atom is $13.6\, \mathrm{eV}$, then, the energy required to remove the electron from the second excited state of $\mathrm{Li}^{2+}$ will be : $x \times 10^{-1} \mathrm{eV
The waves emitted when a metal target is bombarded with high energy electrons are
A small particle of mass $m$ moves in such a way that its potential energy $U=\frac{1}{2} m ~\omega^{2} r^{2}$ where $\omega$ is constant and $r$ is the distance of the particle from origin. Assuming Bohr's quantization of momentu
The angular momentum for the electron in Bohr's orbit is L. If the electron is assumed to revolve in second orbit of hydrogen atom, then the change in angular momentum will be
The energy of $\mathrm{He}^{+}$ ion in its first excited state is, (The ground state energy for the Hydrogen atom is $-13.6 ~\mathrm{eV})$ :
The ratio of the magnitude of the kinetic energy to the potential energy of an electron in the $5^{th}$ excited state of a hydrogen atom is :
The ratio of the shortest wavelength of Balmer series to the shortest wavelength of Lyman series for hydrogen atom is :
In Rutherford's alpha-particle scattering experiment, only a few alpha particles rebound back because A. The size of gold nucleus is very small as compared to the size of gold atom. B. Alpha particle and gold nucleus have equal ch
Angular momentum of an electron in a hydrogen atom is $\frac{3h}{\pi}$, then the energy of the electron is _____ eV.
The ratio of momentum of the photons of the $1^{\text {st }}$ and $2^{\text {nd }}$ line of Balmer series of Hydrogen atoms is $\alpha / \beta$. The possible values of $\alpha$ and $\beta$ are:-
Using Bohr’s model, calculate the ratio of the magnetic fields generated due to the motion of the electrons in the $2^{nd}$ and $4^{th}$ orbits of hydrogen atom ________.
Consider two identical galvanometers and two identical resistors with resistance R. If the internal resistance of the galvanometers RC < R/2, which of the following statement(s) about any one of the galvanometers is(are) true?
Two resistors $R_{1}$ = (4 $\pm$ 0.8) $\Omega$ and $R_{2}$ = (4 $\pm$ 0.4) $\Omega$ are connected in parallel. The equivalent resistance of their parallel combination will be :
For full scale deflection of total 50 divisions, 50 mV voltage is required in galvanometer. The resistance of galvanometer if its current sensitivity is 2 div/mA will be :
A conducting wire of length 'l', area of cross-section A and electric resistivity $\rho$ is connected between the terminals of a battery. A potential difference V is developed between its ends, causing an electric current. If the
An electric bulb of 500 watt at 100 volt is used in a circuit having a 200 V supply. Calculate the resistance R to be connected in series with the bulb so that the power delivered by the bulb is 500 W.
Five identical cells each of internal resistance 1$\Omega$ and emf 5V are connected in series and in parallel with an external resistance 'R'. For what value of 'R', current in series and parallel combination will remain the same?
Consider a galvanometer shunted with 5$\Omega$ resistance and 2% of current passes through it. What is the resistance of the given galvanometer ?
The $\mathrm{H}$ amount of thermal energy is developed by a resistor in $10 \mathrm{~s}$ when a current of $4 \mathrm{~A}$ is passed through it. If the current is increased to $16 \mathrm{~A}$, the thermal energy developed by the
Ratio of thermal energy released in two resistors R and 3R connected in parallel in an electric circuit is :
The number of turns of the coil of a moving coil galvanometer is increased in order to increase current sensitivity by $50 \%$. The percentage change in voltage sensitivity of the galvanometer will be :
A cell of emf 90 V is connected across series combination of two resistors each of 100$\Omega$ resistance. A voltmeter of resistance 400$\Omega$ is used to measure the potential difference across each resistor. The reading of the
With the help of potentiometer, we can determine the value of emf of a given cell. The sensitivity of the potentiometer is (A) directly proportional to the length of the potentiometer wire (B) directly proportional to the potentia
The drift velocity of electrons for a conductor connected in an electrical circuit is $\mathrm{V}_{\mathrm{d}}$. The conductor in now replaced by another conductor with same material and same length but double the area of cross se
A uniform metallic wire carries a current 2 A, when 3.4 V battery is connected across it. The mass of uniform metallic wire is 8.92 $\times$ 10$^{-3}$ kg, density is 8.92 $\times$ 10$^{3}$ kg/m$^3$ and resistivity is 1.7 $\times$
The resistance of a wire is 5 $\Omega$. It's new resistance in ohm if stretched to 5 times of it's original length will be :
When two resistance $\mathrm{R_1}$ and $\mathrm{R_2}$ connected in series and introduced into the left gap of a meter bridge and a resistance of 10 $\Omega$ is introduced into the right gap, a null point is found at 60 cm from lef
In an experiment to find emf of a cell using potentiometer, the length of null point for a cell of emf $1.5 \mathrm{~V}$ is found to be $60 \mathrm{~cm}$. If this cell is replaced by another cell of emf E, the length-of null point
A hollow cylindrical conductor has length of 3.14 m, while its inner and outer diameters are 4 mm and 8 mm respectively. The resistance of the conductor is $n\times10^{-3}\Omega$. If the resistivity of the material is $\mathrm{2.4
If a copper wire is stretched to increase its length by 20%. The percentage increase in resistance of the wire is __________%.
In a metre bridge experiment the balance point is obtained if the gaps are closed by 2$\Omega$ and 3$\Omega$. A shunt of X $\Omega$ is added to 3$\Omega$ resistor to shift the balancing point by 22.5 cm. The value of X is ________
A null point is found at 200 cm in potentiometer when cell in secondary circuit is shunted by 5$\Omega$. When a resistance of 15$\Omega$ is used for shunting, null point moves to 300 cm. The internal resistance of the cell is ____
Two identical cells, when connected either in parallel or in series gives same current in an external resistance $5 ~\Omega$. The internal resistance of each cell will be ___________ $\Omega$.
Two identical heater filaments are connected first in parallel and then in series. At the same applied voltage, the ratio of heat produced in same time for parallel to series will be:
Given below are two statements: Statement I : The equivalent resistance of resistors in a series combination is smaller than least resistance used in the combination. Statement II : The resistivity of the material is independent o
The current sensitivity of moving coil galvanometer is increased by $25 \%$. This increase is achieved only by changing in the number of turns of coils and area of cross section of the wire while keeping the resistance of galvanom
When a resistance of $5 ~\Omega$ is shunted with a moving coil galvanometer, it shows a full scale deflection for a current of $250 \mathrm{~mA}$, however when $1050 ~\Omega$ resistance is connected with it in series, it gives ful
The length of a metallic wire is increased by $20 \%$ and its area of cross section is reduced by $4 \%$. The percentage change in resistance of the metallic wire is __________.
The number density of free electrons in copper is nearly $8 \times 10^{28} \mathrm{~m}^{-3}$. A copper wire has its area of cross section $=2 \times 10^{-6} \mathrm{~m}^{2}$ and is carrying a current of $3.2 \mathrm{~A}$. The drif
10 resistors each of resistance 10 $\Omega$ can be connected in such as to get maximum and minimum equivalent resistance. The ratio of maximum and minimum equivalent resistance will be ___________.
A potential $\mathrm{V}_{0}$ is applied across a uniform wire of resistance $R$. The power dissipation is $P_{1}$. The wire is then cut into two equal halves and a potential of $V_{0}$ is applied across the length of each half. Th
A current of $2 \mathrm{~A}$ flows through a wire of cross-sectional area $25.0 \mathrm{~mm}^{2}$. The number of free electrons in a cubic meter are $2.0 \times 10^{28}$. The drift velocity of the electrons is __________ $\times 1
Two identical cells each of emf $1.5 \mathrm{~V}$ are connected in series across a $10 ~\Omega$ resistance. An ideal voltmeter connected across $10 ~\Omega$ resistance reads $1.5 \mathrm{~V}$. The internal resistance of each cell
A voltmeter with internal resistance of $x \Omega$ can be used to measure upto 20 V . In order to increase its measuring range to 30 V , the required modification is to $\_\_\_\_$ .
Two resistors of 200 $\Omega$ and 400 $\Omega$ are connected in series with a battery of 100 V. A bulb rated at 200 V, 100 W is connected across the 400 $\Omega$ resistance. The potential drop across the bulb is ________ V.
When an external resistance of $5 \Omega$ is connected across terminals of a cell, a current of 0.25 A flows through it. When the $5 \Omega$ resistor is replaced by a $2 \Omega$ resistor, a current of 0.5 A flows through it. The i
Two cells of emfs 1 V and 2 V and internal resistance $2 \Omega$ and $1 \Omega$, respectively connected in parallel, gave a current of 1 A through an external resistance. If the polarity of one cell is reversed, then value of curr
An electron (of mass m) and a photon have the same energy E in the range of a few eV. The ratio of the de-Broglie wavelength associated with the electron and the wavelength of the photon is (c = speed of light in vaccuum)
An electron of mass m and magnitude of charge |e| initially at rest gets accelerated by a constant electric field E. The rate of change of de-Broglie wavelength of this electron at time t ignoring relativistic effects is :
The surface of a metal is illuminated alternately with photons of energies $E_{1}$ = 4 eV and $E_{2}$ = 2.5 eV respectively. The ratio of maximum speeds of the photoelectrons emitted in the two cases is 2. The work function of the
Two sources of light emit X-rays of wavelength 1 nm and visible light of wavelength 500 nm, respectively. Both the sources emit light of the same power 200 W. The ratio of the number density of photons of X-rays to the number dens
When photon of energy 4.0 eV strikes the surface of a metal A, the ejected photoelectrons have maximum kinetic energy $T_{A}$ eV end de-Broglie wavelength $\lambda _A$. The maximum kinetic energy of photoelectrons liberated from a
When the wavelength of radiation falling on a metal is changed from 500 nm to 200 nm, the maximum kinetic energy of the photoelectrons becomes three times larger. The work function of the metal is close to :
An electron of mass $m_{e}$ and a proton of mass $m_{p}$ = 1836 $m_{e}$ are moving with the same speed. The ratio of their de Broglie wavelength ${{{}^\lambda electron} \over {{}^\lambda proton}}$ will be :
The stopping potential for electrons emitted from a photosensitive surface illuminated by light of wavelength 491 nm is 0.710 V. When the incident wavelength is changed to a new value, the stopping potential is 1.43 V. The new wav
Given below are two statements : Statement I : Two photons having equal linear momenta have equal wavelengths. Statement II : If the wavelength of photon is decreased, then the momentum and energy of a photon will also decrease. I
An $\alpha$ particle and a proton are accelerated from rest through the same potential difference. The ratio of linear momenta acquired by above two particles will be:
An $\alpha$ particle and a carbon 12 atom has same kinetic energy K. The ratio of their de-Broglie wavelengths $({\lambda _\alpha }:{\lambda _{C12}})$ is :
Given below are two statements : Statement I : Davisson-Germer experiment establishes the wave nature of electrons. Statement II : If electrons have wave nature, they can interfere and show diffraction. In the light of the above s
The kinetic energy of emitted electron is E when the light incident on the metal has wavelength $\lambda$. To double the kinetic energy, the incident light must have wavelength:
A metal exposed to light of wavelength $800 \mathrm{~nm}$ and and emits photoelectrons with a certain kinetic energy. The maximum kinetic energy of photo-electron doubles when light of wavelength $500 \mathrm{~nm}$ is used. The wo
With reference to the observations in photo-electric effect, identify the correct statements from below : (A) The square of maximum velocity of photoelectrons varies linearly with frequency of incident light. (B) The value of satu
Two streams of photons, possessing energies equal to five and ten times the work function of metal are incident on the metal surface successively. The ratio of maximum velocities of the photoelectron emitted, in the two cases resp
An electron with speed v and a photon with speed c have the same de-Broglie wavelength. If the kinetic energy and momentum of electron are $E_{e}$ and $p_{e}$ and that of photon are $E_{ph}$ and $p_{ph}$ respectively. Which of the
A metal surface is illuminated by a radiation of wavelength 4500 $\overset{\circ}{A}$. The ejected photo-electron enters a constant magnetic field of 2 mT making an angle of 90$^\circ$ with the magnetic field. If it starts revolvi
A parallel beam of light of wavelength $900 \mathrm{~nm}$ and intensity $100 \,\mathrm{Wm}^{-2}$ is incident on a surface perpendicular to the beam. The number of photons crossing $1 \mathrm{~cm}^{2}$ area perpendicular to the bea
The ratio of wavelengths of proton and deuteron accelerated by potential $V_{p}$ and $V_{d}$ is 1 : $\sqrt2$. Then the ratio of $V_{p}$ to $V_{d}$ will be :
Given below are two statements : one is labelled as Assertion A and the other is labelled as Reason R : Assertion A : The photoelectric effect does not takes place, if the energy of the incident radiation is less than the work fun
The ratio of the de-Broglie wavelengths of proton and electron having same Kinetic energy : (Assume $m_{p}=m_{e} \times 1849$ )
Proton $(\mathrm{P})$ and electron (e) will have same de-Broglie wavelength when the ratio of their momentum is (assume, $\mathrm{m}_{\mathrm{p}}=1849 \mathrm{~m}_{\mathrm{e}}$ ):
Given below are two statements: Statement I : Out of microwaves, infrared rays and ultraviolet rays, ultraviolet rays are the most effective for the emission of electrons from a metallic surface. Statement II : Above the threshold
The work functions of Aluminium and Gold are $4.1 ~\mathrm{eV}$ and and $5.1 ~\mathrm{eV}$ respectively. The ratio of the slope of the stopping potential versus frequency plot for Gold to that of Aluminium is
In photo electric effect A. The photocurrent is proportional to the intensity of the incident radiation B. Maximum Kinetic energy with which photoelectrons are emitted depends on the intensity of incident light. C. Max. K.E with w
A monochromatic light is incident on a hydrogen sample in ground state. Hydrogen atoms absorb a fraction of light and subsequently emit radiation of six different wavelengths. The frequency of incident light is $x \times 10^{15} \
An atom absorbs a photon of wavelength $500 \mathrm{~nm}$ and emits another photon of wavelength $600 \mathrm{~nm}$. The net energy absorbed by the atom in this process is $n \times 10^{-4} ~\mathrm{eV}$. The value of n is _______
The de Broglie wavelength for an electron accelerated through the potential difference of $V_1$ volt is $\lambda_1$. When the potential difference is changed to $V_2$ volt, the associated de Broglie wavelength is increased by $50
The threshold frequency of a metal with work function $6.63 \mathrm{~eV}$ is :
For a certain metal, when monochromatic light of wavelength $\lambda$ is incident, the stopping potential for photoelectrons is $3V_0$. When the same metal is illuminated by light of wavelength $2\lambda$, then the stopping potent
An electron is travelling with a velocity $v$ in free space and when it enters a medium, its velocity is reduced by $20 \%$. The de Broglie wavelength of electron in the medium is $\alpha \lambda_0$, where $\lambda_0$ is its de Br
The de Broglie wavelength associated with an electron accelerated through a potential difference V is $\lambda_{\mathrm{e}}$ and the de Broglie wavelength associated with a proton accelerated through the same potential difference
Two isolated conducting spheres $S_{1}$ and $S_{2}$ of radius ${2 \over 3}R$ and ${1 \over 3}R$ have 12 $\mu$C and –3 $\mu$C charges, respectively, and are at a large distance from each other. They are now connected by a conductin
A parallel plate capacitor has plate of length 'l', width ‘w’ and separation of plates is ‘d’. It is connected to a battery of emf V. A dielectric slab of the same thickness ‘d’ and of dielectric constant k = 4 is being inserted b
Concentric metallic hollow spheres of radii R and 4R hold charges $Q_{1}$ and $Q_{2}$ respectively. Given that surface charge densities of the concentric spheres are equal, the potential difference V(R) – V(4R) is :
A 10 $\mu$F capacitor is fully charged to a potential difference of 50 V. After removing the source voltage it is connected to an uncharged capacitor in parallel. Now the potential difference across them becomes 20 V. The capacita
A 60 pF capacitor is fully charged by a 20 V supply. It is then disconnected from the supply and is conneced to another uncharged 60 pF capacitor in parallel. The electrostatic energy that is lost in this process by the time the c
Ten charges are placed on the circumference of a circle of radius R with constant angular separation between successive charges. Alternate charges 1, 3, 5, 7, 9 have charge (+q) each, while 2, 4, 6, 8, 10 have charge (–q) each. Th
Two capacitors of capacitances C and 2C are charged to potential differences V and 2V, respectively. These are then connected in parallel in such a manner that the positive terminal of one is connected to the negative terminal of
Effective capacitance of parallel combination of two capacitors $C_{1}$ and $C_{2}$ is 10 $\mu$F. When these capacitors are individually connected to a voltage source of 1V, the energy stored in the capacitor $C_{2}$ is 4 times th
An electron with kinetic energy $K_{1}$ enters between parallel plates of a capacitor at an angle '$\alpha$' with the plates. It leaves the plates at angle '$\beta$' with kinetic energy $K_{2}$. Then the ratio of kinetic energies
Two equal capacitors are first connected in series and then in parallel. The ratio of the equivalent capacities in the two cases will be :
Two capacitors, each having capacitance $40 \,\mu \mathrm{F}$ are connected in series. The space between one of the capacitors is filled with dielectric material of dielectric constant $\mathrm{K}$ such that the equivalence capaci
Sixty four conducting drops each of radius 0.02 m and each carrying a charge of 5 $\mu$C are combined to form a bigger drop. The ratio of surface density of bigger drop to the smaller drop will be :
The total charge on the system of capacitors $C_{1}=1 \mu \mathrm{F}, C_{2}=2 \mu \mathrm{F}, \mathrm{C}_{3}=4 \mu \mathrm{F}$ and $\mathrm{C}_{4}=3 \mu \mathrm{F}$ connected in parallel is : (Assume a battery of $20 \mathrm{~V}$
Given below are two statements. Statement I : Electric potential is constant within and at the surface of each conductor. Statement II : Electric field just outside a charged conductor is perpendicular to the surface of the conduc
A force of 10 N acts on a charged particle placed between two plates of a charged capacitor. If one plate of capacitor is removed, then the force acting on that particle will be.
A parallel plate capacitor filled with a medium of dielectric constant 10, is connected across a battery and is charged. The dielectric slab is replaced by another slab of dielectric constant 15. Then the energy of capacitor will
Two identical thin metal plates has charge $q_{1}$ and $q_{2}$ respectively such that $q_{1}>q_{2}$. The plates were brought close to each other to form a parallel plate capacitor of capacitance C. The potential difference between
Capacitance of an isolated conducting sphere of radius $R_{1}$ becomes n times when it is enclosed by a concentric conducting sphere of radius $R_{2}$ connected to earth. The ratio of their radii $\left( {{{{R_2}} \over {{R_1}}}}
A capacitor is discharging through a resistor R. Consider in time $t_{1}$, the energy stored in the capacitor reduces to half of its initial value and in time $t_{2}$, the charge stored reduces to one eighth of its initial value.
Two metallic plates form a parallel plate capacitor. The distance between the plates is 'd'. A metal sheet of thickness ${d \over 2}$ and of area equal to area of each plate is introduced between the plates. What will be the ratio
A slab of dielectric constant $\mathrm{K}$ has the same cross-sectional area as the plates of a parallel plate capacitor and thickness $\frac{3}{4} \mathrm{~d}$, where $\mathrm{d}$ is the separation of the plates. The capacitance
A capacitor of capacitance $900 \mu \mathrm{F}$ is charged by a $100 \mathrm{~V}$ battery. The capacitor is disconnected from the battery and connected to another uncharged identical capacitor such that one plate of uncharged capa
A parallel plate capacitor with air between the plate has a capacitance of 15pF. The separation between the plate becomes twice and the space between them is filled with a medium of dielectric constant 3.5. Then the capacitance be
For a charged spherical ball, electrostatic potential inside the ball varies with $r$ as $\mathrm{V}=2ar^2+b$. Here, $a$ and $b$ are constant and r is the distance from the center. The volume charge density inside the ball is $-\l
Two parallel plate capacitors $C_{1}$ and $C_{2}$ each having capacitance of $10 \mu \mathrm{F}$ are individually charged by a 100 V D.C. source. Capacitor $C_{1}$ is kept connected to the source and a dielectric slab is inserted
The distance between two plates of a capacitor is $\mathrm{d}$ and its capacitance is $\mathrm{C}_{1}$, when air is the medium between the plates. If a metal sheet of thickness $\frac{2 d}{3}$ and of the same area as plate is intr
A parallel plate capacitor of capacitance $2 \mathrm{~F}$ is charged to a potential $\mathrm{V}$, The energy stored in the capacitor is $E_{1}$. The capacitor is now connected to another uncharged identical capacitor in parallel c
A capacitor of capacitance $\mathrm{C}$ is charged to a potential V. The flux of the electric field through a closed surface enclosing the positive plate of the capacitor is :
A $600 ~\mathrm{pF}$ capacitor is charged by $200 \mathrm{~V}$ supply. It is then disconnected from the supply and is connected to another uncharged $600 ~\mathrm{pF}$ capacitor. Electrostatic energy lost in the process is _______
Two charged conducting spheres $S_1$ and $S_2$ of radii 8 cm and 18 cm are connected to each other by a wire. After equilibrium is established, the ratio of electric fields on $S_1$ and $S_2$ spheres are $E_{S1}$ and $E_{S2}$ resp
The electric potential as a function of $x, y$ is given by $V=5\left(x^2-y^2\right) V$. The electric field at a point $(2,3) \mathrm{m}$ is $\_\_\_\_ \mathrm{V} / \mathrm{m}$.
A sphere of capacitance 100 pF is charged to a potential of 100 V . Another identical uncharged metal sphere is brought in contact with the charged sphere, then the change in the total energy stored on these spheres, when they tou
A parallel plate capacitor is having separation between plates 0.885 mm . It has a capacitance of $1 \mu \mathrm{~F}$ when the space between the plates is filled with an insulating material of resistivity $1 \times 10^{13} \Omega
A three coulomb charge moves from the point $(0,-2,-5)$ to the point $(5,1,2)$ in an electric field expressed as $\vec{E}=2 x \hat{\mathrm{i}}+3 \mathrm{y}^2 \hat{\mathrm{j}}+4 \hat{\mathrm{k}} \mathrm{N} / \mathrm{C}$. The work d
A uniformly charged disc of radius R having surface charge density $\sigma$ is placed in the xy plane with its center at the origin. Find the electric field intensity along the z-axis at a distance Z from origin :-
Choose the incorrect statement : (1) The electric lines of force entering into a Gaussian surface provide negative flux. (2) A charge 'q' is placed at the centre of a cube. The flux through all the faces will be the same. (3) In a
Two identical tennis balls each having mass 'm' and charge 'q' are suspended from a fixed point by threads of length 'l'. What is the equilibrium separation when each thread makes a small angle '$\theta$' with the vertical?
A point charge of 10 $\mu$C is placed at the origin. At what location on the X-axis should a point charge of 40 $\mu$C be placed so that the net electric field is zero at $x=2$cm on the X-axis?
A point charge $2\times10^{-2}~\mathrm{C}$ is moved from P to S in a uniform electric field of $30~\mathrm{NC^{-1}}$ directed along positive x-axis. If coordinates of P and S are (1, 2, 0) m and (0, 0, 0) m respectively, the work
Two isolated metallic solid spheres of radii $\mathrm{R}$ and $2 \mathrm{R}$ are charged such that both have same charge density $\sigma$. The spheres are then connected by a thin conducting wire. If the new charge density of the
If two charges q$_1$ and q$_2$ are separated with distance 'd' and placed in a medium of dielectric constant K. What will be the equivalent distance between charges in air for the same electrostatic force?
Two equal positive point charges are separated by a distance $2 a$. The distance of a point from the centre of the line joining two charges on the equatorial line (perpendicular bisector) at which force experienced by a test charg
A point charge $q_1=4q_0$ is placed at origin. Another point charge $q_2=-q_0$ is placed at $x=12$ cm. Charge of proton is $q_0$. The proton is placed on $x$ axis so that the electrostatic force on the proton is zero. In this situ
A stream of a positively charged particles having ${q \over m} = 2 \times {10^{11}}{C \over {kg}}$ and velocity ${\overrightarrow v _0} = 3 \times {10^7}\widehat i\,m/s$ is deflected by an electric field $1.8\widehat j$ kV/m. The
The electric field due to a short electric dipole at a large distance $(r)$ from center of dipole on the equatorial plane varies with distance as :
In a metallic conductor, under the effect of applied electric field, the free electrons of the conductor
A dipole comprises of two charged particles of identical magnitude $q$ and opposite in nature. The mass 'm' of the positive charged particle is half of the mass of the negative charged particle. The two charges are separated by a
Two charges each of magnitude $0.01 ~\mathrm{C}$ and separated by a distance of $0.4 \mathrm{~mm}$ constitute an electric dipole. If the dipole is placed in an uniform electric field '$\vec{E}$' of 10 dyne/C making $30^{\circ}$ an
A $10 ~\mu \mathrm{C}$ charge is divided into two parts and placed at $1 \mathrm{~cm}$ distance so that the repulsive force between them is maximum. The charges of the two parts are:
A thin infinite sheet charge and an infinite line charge of respective charge densities $+\sigma$ and $+\lambda$ are placed parallel at $5 \mathrm{~m}$ distance from each other. Points 'P' and 'Q' are at $\frac{3}{\pi}$ m and $\fr
A rigid dipole undergoes a simple harmonic motion about its centre in the presence of an electric field $\overrightarrow{\mathrm{E}}_1=\mathrm{E}_0 \hat{x}$. If another electric field $\overrightarrow{\mathrm{E}}_2=2 \mathrm{E}_0(
Given below are two statements: one is labelled as Assertion A and the other is labelled as Reason $\mathbf{R}$ Assertion A : In electrostatics, a conductor does not store any net charge inside. Reason R : Inside the capacitor (wi
A thin half ring of radius 35 cm is uniformly charged with a total charge of $Q$ coulomb. If the magnitude of the electric field at centre of the half ring is $100 \mathrm{~V} / \mathrm{m}$, then the value of $Q$ is $\_\_\_\_$ nC
Two point charges $8\ \mu C$ and $-2\ \mu C$ are located at $x = 2$ cm and $x = 4$ cm, respectively on the $x$-axis. The ratio of electric flux due to these charges through two spheres of radii 3 cm and 5 cm with their centers at
Two point charges $\mathrm{q}_1=3 \mu C$ and $\mathrm{q}_2=-4 \mu C$ are placed at points $(2 \hat{i}+3 \hat{j}+3 \hat{k})$ and $(\hat{i}+\hat{j}+\hat{k})$ respectively. Force on charge $\mathrm{q}_2$ is $\_\_\_\_$ N. (Take $\frac
Inside a uniform spherical shell : (1) the gravitational field is zero (2) the gravitational potential is zero (3) the gravitational field is same everywhere (4) the gravitational potential is same everywhere (5) all of the above
The masses and radii of the earth and moon are ($M_{1}$, $R_{1}$) and ($M_{2}$, $R_{2}$) respectively. Their centres are at a distance 'r' apart. Find the minimum escape velocity for a particle of mass 'm' to be projected from the
A mass of 50 kg is placed at the centre of a uniform spherical shell of mass 100 kg and radius 50 m. If the gravitational potential at a point, 25 m from the centre is V kg/m. The value of V is :
Given below are two statements: Statement I: Acceleration due to gravity is different at different places on the surface of earth. Statement II: Acceleration due to gravity increases as we go down below the earth's surface. In the
The weight of a body at the surface of earth is 18 N. The weight of the body at an altitude of 3200 km above the earth's surface is (given, radius of earth $\mathrm{R_e=6400~km}$) :
If the distance of the earth from Sun is 1.5 $\times$ 10$^6$ km. Then the distance of an imaginary planet from Sun, if its period of revolution is 2.83 years is :
Assume that the earth is a solid sphere of uniform density and a tunnel is dug along its diameter throughout the earth. It is found that when a particle is released in this tunnel, it executes a simple harmonic motion. The mass of
If earth has a mass nine times and radius twice to that of a planet P. Then $\frac{v_{e}}{3} \sqrt{x} \mathrm{~ms}^{-1}$ will be the minimum velocity required by a rocket to pull out of gravitational force of $\mathrm{P}$, where $
Given below are two statements: Statement I : Acceleration due to earth's gravity decreases as you go 'up' or 'down' from earth's surface. Statement II : Acceleration due to earth's gravity is same at a height 'h' and depth 'd' fr
A body weight $\mathrm{W}$, is projected vertically upwards from earth's surface to reach a height above the earth which is equal to nine times the radius of earth. The weight of the body at that height will be :
Two particles of equal mass '$m$' move in a circle of radius '$r$' under the action of their mutual gravitational attraction. The speed of each particle will be :
A body of mass is taken from earth surface to the height h equal to twice the radius of earth (R$_e$), the increase in potential energy will be : (g = acceleration due to gravity on the surface of Earth)
At a certain depth "d " below surface of earth, value of acceleration due to gravity becomes four times that of its value at a height $\mathrm{3 R}$ above earth surface. Where $\mathrm{R}$ is Radius of earth (Take $\mathrm{R}=6400
Given below are two statements: one is labelled as Assertion A and the other is labelled as Reason R. Assertion A : A pendulum clock when taken to Mount Everest becomes fast. Reason R : The value of g (acceleration due to gravity)
The time period of a satellite of earth is 24 hours. If the separation between the earth and the satellite is decreased to one fourth of the previous value, then its new time period will become.
An object is allowed to fall from a height $R$ above the earth, where $R$ is the radius of earth. Its velocity when it strikes the earth's surface, ignoring air resistance, will be
Every planet revolves around the sun in an elliptical orbit :- A. The force acting on a planet is inversely proportional to square of distance from sun. B. Force acting on planet is inversely proportional to product of the masses
Given below are two statements: Statement I : Rotation of the earth shows effect on the value of acceleration due to gravity (g) Statement II : The effect of rotation of the earth on the value of 'g' at the equator is minimum and
Given below are two statements : one is labelled as Assertion $\mathbf{A}$ and the other is labelled as Reason $\mathbf{R}$. Assertion A : Earth has atmosphere whereas moon doesn't have any atmosphere. Reason R : The escape veloci
The orbital angular momentum of a satellite is L, when it is revolving in a circular orbit at height h from earth surface. If the distance of satellite from the earth centre is increased by eight times to its initial value, then t
The time period of a satellite, revolving above earth's surface at a height equal to $\mathrm{R}$ will be (Given $g=\pi^{2} \mathrm{~m} / \mathrm{s}^{2}, \mathrm{R}=$ radius of earth)
A space ship of mass $2 \times 10^{4} \mathrm{~kg}$ is launched into a circular orbit close to the earth surface. The additional velocity to be imparted to the space ship in the orbit to overcome the gravitational pull will be (if
The weight of a body on the earth is $400 \mathrm{~N}$. Then weight of the body when taken to a depth half of the radius of the earth will be:
Two satellites of masses m and 3m revolve around the earth in circular orbits of radii r & 3r respectively. The ratio of orbital speeds of the satellites respectively is
Two planets A and B of radii $\mathrm{R}$ and 1.5 R have densities $\rho$ and $\rho / 2$ respectively. The ratio of acceleration due to gravity at the surface of $\mathrm{B}$ to $\mathrm{A}$ is:
Assuming the earth to be a sphere of uniform mass density, the weight of a body at a depth $d=\frac{R}{2}$ from the surface of earth, if its weight on the surface of earth is 200 N, will be: (Given R = radius of earth)
The acceleration due to gravity at height $h$ above the earth if $h << \mathrm{R}$ (Radius of earth) is given by
Two identical particles each of mass ' $m$ ' go round a circle of radius $a$ under the action of their mutual gravitational attraction. The angular speed of each particle will be :
A body is released from a height equal to the radius $(\mathrm{R})$ of the earth. The velocity of the body when it strikes the surface of the earth will be (Given $g=$ acceleration due to gravity on the earth.)
The weight of a body on the surface of the earth is $100 \mathrm{~N}$. The gravitational force on it when taken at a height, from the surface of earth, equal to one-fourth the radius of the earth is:
Given below are two statements: Statement I : For a planet, if the ratio of mass of the planet to its radius increases, the escape velocity from the planet also increases. Statement II : Escape velocity is independent of the radiu
A planet has double the mass of the earth. Its average density is equal to that of the earth. An object weighing $\mathrm{W}$ on earth will weigh on that planet:
Given below are two statements: Statement I: If $\mathrm{E}$ be the total energy of a satellite moving around the earth, then its potential energy will be $\frac{E}{2}$. Statement II: The kinetic energy of a satellite revolving in
If $\mathrm{V}$ is the gravitational potential due to sphere of uniform density on it's surface, then it's value at the center of sphere will be:-
A planet having mass $9 \mathrm{Me}$ and radius $4 \mathrm{R}_{\mathrm{e}}$, where $\mathrm{Me}$ and $\mathrm{Re}$ are mass and radius of earth respectively, has escape velocity in $\mathrm{km} / \mathrm{s}$ given by: (Given escap
If the earth suddenly shrinks to $\frac{1}{64}$th of its original volume with its mass remaining the same, the period of rotation of earth becomes $\frac{24}{x}$h. The value of x is __________.
When one moves from a point 16 km below the earth's surface to a point 16 km above the earth's surface. The change in g is approximately $\alpha \%$. The value of $\alpha$ is $\_\_\_\_$ . (Take radius of the earth $=6400 \mathrm{~
A planet ($P_1$) is moving around the star of mass $2M$ in the orbit of radius $R$. Another planet ($P_2$) is moving around another star of mass $4M$ in a orbit of radius $2R$. Ratio of time periods of revolution of $P_2$ and $P_1
The height in terms of radius of the earth $(R)$, at which the acceleration due to gravity becomes $\frac{g}{9}$, where $g$ is acceleration due to gravity on earth's surface, is $\_\_\_\_$ .
If a body of mass 1 kg falls on the earth from infinity, it attains velocity ( v ) and kinetic energy ( k ) on reaching the surface of earth. The values of v and k respectively are __________. (Take radius of earth to be 6400 km a
A body of mass $m$ is taken from the surface of earth to a height equal to twice the radius of earth $\left(R_e\right)$. The increase in potential energy will be $\_\_\_\_$ . ( $g$ is acceleration due to gravity at the surface of
A gas mixture consists of 3 moles of oxygen and 5 moles of argon at temperature T. considering only translational and rotational modes, the total internal energy of the system is :
Two gases-argon (atomic radius 0.07 nm, atomic weight 40) and xenon (atomic radius 0.1 nm, atomic weight 140) have the same number density and are at the same temperature. The raito of their respective mean free times is closest t
Consider a mixture of n moles of helium gas and 2n moles of oxygen gas (molecules taken to be rigid) as an ideal gas. Its $C_{P}$/$C_{V}$ value will be :
To raise the temperature of a certain mass of gas by $50^{o}$C at a constant pressure, 160 calories of heat is required. When the same mass of gas is cooled by $100^{o}$C at constant volume, 240 calories of heat is released. How m
Molecules of an ideal gas are known to have three translational degrees of freedom and two rotational degrees of freedom.The gas is maintained at a temperature of T. The total internal energy, U of a mole of this gas, and the valu
An ideal gas in a closed container is slowly heated. As its temperature increases, which of the following statements are true? (A) the mean free path of the molecules decreases. (B) the mean collision time between the molecules de
The change in the magnitude of the volume of an ideal gas when a small additional pressure $\Delta$P is applied at a constant temperature, is the same as the change when the temperature is reduced by a small quantity $\Delta$T at
Initially a gas of diatomic molecules is contained in a cylinder of volume $V_{1}$ at a pressure $P_{1}$ and temperature 250 K. Assuming that 25% of the molecules get dissociated causing a change in number of moles. The pressure o
Under an adiabatic process, the volume of an ideal gas gets doubled. Consequently the mean collision time between the gas molecule changes from ${\tau _1}$ to ${\tau _2}$ . If ${{{C_p}} \over {{C_v}}} = \gamma$ for this gas then a
Given below are two statements : Statement I : In a diatomic molecule, the rotational energy at a given temperature obeys Maxwell's distribution. Statement II : In a diatomic molecule, the rotational energy at a given temperature
What will be the average value of energy along one degree of freedom for an ideal gas in thermal equilibrium at a temperature T? ($k_{B}$ is Boltzmann constant)
A gas has $n$ degrees of freedom. The ratio of specific heat of gas at constant volume to the specific heat of gas at constant pressure will be :
7 mol of a certain monoatomic ideal gas undergoes a temperature increase of $40 \mathrm{~K}$ at constant pressure. The increase in the internal energy of the gas in this process is : (Given $\mathrm{R}=8.3 \,\mathrm{JK}^{-1} \math
A vessel contains 16g of hydrogen and 128g of oxygen at standard temperature and pressure. The volume of the vessel in $cm^{3}$ is :
Sound travels in a mixture of two moles of helium and n moles of hydrogen. If rms speed of gas molecules in the mixture is $\sqrt2$ times the speed of sound, then the value of n will be :
The root mean square speed of smoke particles of mass $5 \times 10^{-17} \mathrm{~kg}$ in their Brownian motion in air at NTP is approximately. [Given $\mathrm{k}=1.38 \times 10^{-23} \mathrm{JK}^{-1}$]
The relation between root mean square speed ($v_{rms}$) and most probable sped ($v_{p}$) for the molar mass M of oxygen gas molecule at the temperature of 300 K will be :
A flask contains argon and oxygen in the ratio of 3 : 2 in mass and the mixture is kept at 27$^\circ$C. The ratio of their average kinetic energy per molecule respectively will be :
Given below are two statements : Statement I : The average momentum of a molecule in a sample of an ideal gas depends on temperature. Statement II : The rms speed of oxygen molecules in a gas is $v$. If the temperature is doubled
A vessel contains $14 \mathrm{~g}$ of nitrogen gas at a temperature of $27^{\circ} \mathrm{C}$. The amount of heat to be transferred to the gas to double the r.m.s speed of its molecules will be : Take $\mathrm{R}=8.32 \mathrm{~J}
According to kinetic theory of gases, A. The motion of the gas molecules freezes at 0$^\circ$C. B. The mean free path of gas molecules decreases if the density of molecules is increased. C. The mean free path of gas molecules incr
Same gas is filled in two vessels of the same volume at the same temperature. If the ratio of the number of molecules is $1: 4$, then A. The r.m.s. velocity of gas molecules in two vessels will be the same. B. The ratio of pressur
Which statements are correct about degrees of freedom ? (A) A molecule with n degrees of freedom has n$^{2}$ different ways of storing energy. (B) Each degree of freedom is associated with $\frac{1}{2}$ RT average energy per mole.
A thermally insulated vessel contains an ideal gas of molecular mass M and ratio of specific heats 1.4. Vessel is moving with speed v and is suddenly brought to rest. Assuming no heat is lost to the surrounding and vessel temperat
What will be the effect on the root mean square velocity of oxygen molecules if the temperature is doubled and oxygen molecule dissociates into atomic oxygen?
The temperature of an ideal gas is increased from $200 \mathrm{~K}$ to $800 \mathrm{~K}$. If r.m.s. speed of gas at $200 \mathrm{~K}$ is $v_{0}$. Then, r.m.s. speed of the gas at $800 \mathrm{~K}$ will be:
Three vessels of equal volume contain gases at the same temperature and pressure. The first vessel contains neon (monoatomic), the second contains chlorine (diatomic) and third contains uranium hexafloride (polyatomic). Arrange th
The ratio of speed of sound in hydrogen gas to the speed of sound in oxygen gas at the same temperature is:
The mean free path of molecules of a certain gas at STP is $1500 \mathrm{~d}$, where $\mathrm{d}$ is the diameter of the gas molecules. While maintaining the standard pressure, the mean free path of the molecules at $373 \mathrm{~
The number of air molecules per cm$^3$ increased from $3\times10^{19}$ to $12\times10^{19}$. The ratio of collision frequency of air molecules before and after the increase in number respectively is:
A gas mixture consists of 2 moles of oxygen and 4 moles of neon at temperature T. Neglecting all vibrational modes, the total internal energy of the system will be,
The temperature at which the kinetic energy of oxygen molecules becomes double than its value at $27^{\circ} \mathrm{C}$ is
The root mean square speed of molecules of nitrogen gas at $27^{\circ} \mathrm{C}$ is approximately : (Given mass of a nitrogen molecule $=4.6 \times 10^{-26} \mathrm{~kg}$ and take Boltzmann constant $\mathrm{k}_{\mathrm{B}}=1.4
The initial pressure and volume of an ideal gas are P$_0$ and V$_0$. The final pressure of the gas when the gas is suddenly compressed to volume $\frac{V_0}{4}$ will be : (Given $\gamma$ = ratio of specific heats at constant press
A flask contains Hydrogen and Argon in the ratio $2: 1$ by mass. The temperature of the mixture is $30^{\circ} \mathrm{C}$. The ratio of average kinetic energy per molecule of the two gases ( $\mathrm{K}$ argon/K hydrogen) is : (G
Given below are two statements: one is labelled as Assertion A and the other is labelled as Reason R Assertion A : If the average kinetic energy of $\mathrm{H}_2$ and $\mathrm{O}_2$ molecules, kept in two different sized container
One gas of $n_1$ mole of molecules at temperature $T_1$, volume $V_1$, and pressure $P_1$, and another gas of $n_2$ mole of molecules at temperature $T_2$, volume $V_2$, and pressure $P_2$, are mixed resulting in pressure $P$ and
If 2 mole of an ideal monoatomic gas at temperature $T$, is mixed with 6 mole of another ideal monoatomic gas at temperature $2 T$ then the temperature of mixture is:
The frequency ($\nu$) of an oscillating liquid drop may depend upon radius ($r$) of the drop, density ($\rho$) of liquid and the surface tension (s) of the liquid as $\nu=r^a\rho^b s^c$. The values of a, b and c respectively are
The height of liquid column raised in a capillary tube of certain radius when dipped in liquid A vertically is, $5 \mathrm{~cm}$. If the tube is dipped in a similar manner in another liquid $\mathrm{B}$ of surface tension and dens
A bicycle tyre is filled with air having pressure of $270 ~\mathrm{kPa}$ at $27^{\circ} \mathrm{C}$. The approximate pressure of the air in the tyre when the temperature increases to $36^{\circ} \mathrm{C}$ is
A mercury drop of radius $10^{-3}~\mathrm{m}$ is broken into 125 equal size droplets. Surface tension of mercury is $0.45~\mathrm{Nm}^{-1}$. The gain in surface energy is :
A Spherical ball of radius 1mm and density 10.5 g/cc is dropped in glycerine of coefficient of viscosity 9.8 poise and density 1.5 g/cc. Viscous force on the ball when it attains constant velocity is $3696\times10^{-x}$ N. The val
A fully loaded boeing aircraft has a mass of $5.4\times10^5$ kg. Its total wing area is 500 m$^2$. It is in level flight with a speed of 1080 km/h. If the density of air $\rho$ is 1.2 kg m$^{-3}$, the fractional increase in the sp
A glass tube of uniform internal radius ($r$) has a valve separating the two identical ends. Initially, the valve is in a tightly closed position. End 1 has a hemispherical soap bubble of radius $r$. End 2 has sub-hemispherical so
STATEMENT-1: The stream of water flowing at high speed from a garden hose pipe tends to spread like a fountain when held vertically up, but tends to narrow down when held vertically down. and STATEMENT-2: In any steady flow of an
A small spherical monoatomic ideal gas bubble $\left(\gamma = \dfrac{5}{3}\right)$ is trapped inside a liquid of density $\rho_\ell$. Assume that the bubble does not exchange any heat with the liquid. The bubble contains $n$ moles
A small spherical monoatomic ideal gas bubble $\left(\gamma = \dfrac{5}{3}\right)$ is trapped inside a liquid of density $\rho_\ell$. Assume that the bubble does not exchange any heat with the liquid. The bubble contains $n$ moles
A cylindrical vessel of height 500 mm has an orifice (small hole) at its bottom. The orifice is initially closed and water is filled in it up to height H. Now the top is completely sealed with a cap and the orifice at the bottom i
Two soap bubbles A and B are kept in a closed chamber where the air is maintained at pressure 8 N/m$^2$. The radii of bubbles A and B are 2 cm and 4 cm, respectively. Surface tension of the soap-water used to make bubbles is 0.04
Paragraph: When liquid medicine of density $\rho$ is to be put in the eye, it is done with the help of a dropper. As the bulb on the top of the dropper is pressed, a drop forms at the opening of the dropper. We wish to estimate th
Paragraph: When liquid medicine of density $\rho$ is to be put in the eye, it is done with the help of a dropper. As the bulb on the top of the dropper is pressed, a drop forms at the opening of the dropper. We wish to estimate th
Paragraph: When liquid medicine of density $\rho$ is to be put in the eye, it is done with the help of a dropper. As the bulb on the top of the dropper is pressed, a drop forms at the opening of the dropper. We wish to estimate th
Two solid spheres A and B of equal volumes but of different densities $d_A$ and $d_B$ are connected by a string. They are fully immersed in a fluid of density $d_F$. They get arranged into an equilibrium state with a tension in th
A thin uniform cylindrical shell, closed at both ends, is partially filled with water. It is floating vertically in water in half-submerged state. If $\rho_c$ is the relative density of the material of the shell with respect to wa
A solid sphere of radius $R$ and density $\rho$ is attached to one end of a mass-less spring of force constant $k$. The other end of the spring is connected to another solid sphere of radius $R$ and density $3\rho$. The complete a
A glass capillary tube is of the shape of a truncated cone with an apex angle $\alpha$ so that its two ends have cross sections of different radii. When dipped in water vertically, water rises in it to a height $h$, where the radi
In a spray gun a piston pushes air out of a nozzle. A thin tube of uniform cross section is connected to the nozzle. The other end of the tube is in a small liquid container. As the piston pushes air through the nozzle, the liquid
In a spray gun a piston pushes air out of a nozzle. A thin tube of uniform cross section is connected to the nozzle. The other end of the tube is in a small liquid container. As the piston pushes air through the nozzle, the liquid
A person in a lift is holding a water jar, which has a small hole at the lower end of its side. When the lift is at rest, the water jet coming out of the hole hits the floor of the lift at a distance of $1.2\ \text{m}$ from the pe
A spherical body of radius $R$ consists of a fluid of constant density and is in equilibrium under its own gravity. If $P(r)$ is the pressure at $r$ ($r < R$), then the correct option(s) is(are)
Two spheres $P$ and $Q$ of equal radii have densities $\rho_1$ and $\rho_2$, respectively. The spheres are connected by a massless string and placed in liquids $L_1$ and $L_2$ of densities $\sigma_1$ and $\sigma_2$ and viscosities
Consider two solid spheres P and Q each of density $8$ gm cm$^{-3}$ and diameters $1$ cm and $0.5$ cm, respectively. Sphere P is dropped into a liquid of density $0.8$ gm cm$^{-3}$ and viscosity $\eta = 3$ poiseulles. Sphere Q is
A drop of liquid of radius $R = 10^{-2}\ \text{m}$ having surface tension $S = \dfrac{0.1}{4\pi}\ \text{N m}^{-1}$ divides itself into $K$ identical drops. In this process the total change in the surface energy $\Delta U = 10^{-3}
Consider a thin square plate floating on a viscous liquid in a large tank. The height $h$ of the liquid in the tank is much less than the width of the tank. The floating plate is pulled horizontally with a constant velocity $u_0$.
A uniform capillary tube of inner radius $r$ is dipped vertically into a beaker filled with water. The water rises to a height $h$ in the capillary tube above the water surface in the beaker. The surface tension of water is $\sigm
A cylindrical capillary tube of 0.2 mm radius is made by joining two capillaries T1 and T2 of different materials having water contact angles of $0^\circ$ and $60^\circ$, respectively. The capillary tube is dipped vertically in wa
When water is filled carefully in a glass, one can fill it to a height $h$ above the rim of the glass due to the surface tension of water. To calculate $h$ just before water starts flowing, model the shape of the water above the r
A train with cross-sectional area $S_t$ is moving with speed $v_t$ inside a long tunnel of cross-sectional area $S_0$ ($S_0 = 4S_t$). Assume that almost all the air (density $\rho$) in front of the train flows back between its sid
A hot air balloon is carrying some passengers, and a few sandbags of mass $1\ \mathrm{kg}$ each so that its total mass is $480\ \mathrm{kg}$. Its effective volume giving the balloon its buoyancy is $V$. The balloon is floating at
An open-ended U-tube of uniform cross-sectional area contains water (density $10^3\ \mathrm{kg\ m^{-3}}$). Initially the water level stands at $0.29\ \mathrm{m}$ from the bottom in each arm. Kerosene oil (a water-immiscible liquid
A soft plastic bottle, filled with water of density 1 gm/cc, carries an inverted glass test-tube with some air (ideal gas) trapped as shown in the figure. The test-tube has a mass of 5 gm, and it is made of a thick glass of densit
A soft plastic bottle, filled with water of density 1 gm/cc, carries an inverted glass test-tube with some air (ideal gas) trapped as shown in the figure. The test-tube has a mass of 5 gm, and it is made of a thick glass of densit
An ideal gas of density $\rho = 0.2\ kg\ m^{-3}$ enters a chimney of height $h$ at the rate of $\alpha = 0.8\ kg\ s^{-1}$ from its lower end, and escapes through the upper end. The cross-sectional area of the lower end is $A_1 = 0
A bubble has surface tension $S$. The ideal gas inside the bubble has ratio of specific heats $\gamma = \dfrac{5}{3}$. The bubble is exposed to the atmosphere and it always retains its spherical shape. When the atmospheric pressur
An incompressible liquid is kept in a container having a weightless piston with a hole. A capillary tube of inner radius $0.1$ mm is dipped vertically into the liquid through the airtight piston hole. The air in the container is i
Two large, identical water tanks, 1 and 2, kept on the top of a building of height $H$, are filled with water up to height $h$ in each tank. Both the tanks contain an identical hole of small radius on their sides, close to their b
A spherical soap bubble inside an air chamber at pressure $P_0 = 10^5$ Pa has a certain radius so that the excess pressure inside the bubble is $\Delta P = 144$ Pa. Now, the chamber pressure is reduced to $8P_0/27$ so that the bub
A table tennis ball has radius $(3/2)\times 10^{-2}$ m and mass $(22/7)\times 10^{-3}$ kg. It is slowly pushed down into a swimming pool to a depth of $d = 0.7$ m below the water surface and then released from rest. It emerges fro
Question Stem for Question Nos. 15 and 16: A container of height 2 m, length 2 m and breadth 1 m is made of insulating vertical walls and two large area horizontal metal plates ($M_1$ and $M_2$) which extend far beyond the vertica
The surface tension of a soap bubble is 0.03 N/m. The work done in increasing the diameter of bubble from 2 cm to 6 cm is $\alpha \pi \times 10^{-4}$ J. The value of $\alpha$ is _________. (Take $\pi = 3.14$)
If an air bubble of diameter 2 mm rises steadily through a liquid of density 2000 kg/$m^{3}$ at a rate of 0.5 cm/s, then the coefficient of viscosity of liquid is ______ Poise. (Take g = 10 m/$s^{2}$)
Eight equal drops of water are falling through air with a steady speed of $10 \mathrm{~cm} / \mathrm{s}$. If the drops coalesce, the new velocity is:-
A hydraulic automobile lift is designed to lift vehicles of mass $5000 \mathrm{~kg}$. The area of cross section of the cylinder carrying the load is $250 \mathrm{~cm}^{2}$. The maximum pressure the smaller piston would have to bea
A small ball of mass $\mathrm{M}$ and density $\rho$ is dropped in a viscous liquid of density $\rho_{0}$. After some time, the ball falls with a constant velocity. What is the viscous force on the ball ?
Given below are two statements: one is labelled as Assertion $\mathbf{A}$ and the other is labelled as Reason $\mathbf{R}$ Assertion A: When you squeeze one end of a tube to get toothpaste out from the other end, Pascal's principl
Given below are two statements: Statement I : Pressure in a reservoir of water is same at all points at the same level of water. Statement II : The pressure applied to enclosed water is transmitted in all directions equally. In th
Given below are two statements: one is labelled as Assertion $\mathbf{A}$ and the other is labelled as Reason $\mathbf{R}$ Assertion A : A spherical body of radius $(5 \pm 0.1) \mathrm{mm}$ having a particular density is falling t
An air bubble of volume $1 \mathrm{~cm}^{3}$ rises from the bottom of a lake $40 \mathrm{~m}$ deep to the surface at a temperature of $12^{\circ} \mathrm{C}$. The atmospheric pressure is $1 \times 10^{5} \mathrm{~Pa}$ the density
The surface tension of soap solution is $3.5 \times 10^{-2} \mathrm{~Nm}^{-1}$. The amount of work done required to increase the radius of soap bubble from $10 \mathrm{~cm}$ to $20 \mathrm{~cm}$ is _________ $\times ~10^{-4} \math
There is an air bubble of radius $1.0 \mathrm{~mm}$ in a liquid of surface tension $0.075~ \mathrm{Nm}^{-1}$ and density $1000 \mathrm{~kg} \mathrm{~m}^{-3}$ at a depth of $10 \mathrm{~cm}$ below the free surface. The amount by wh
An air bubble of diameter $6 \mathrm{~mm}$ rises steadily through a solution of density $1750 \mathrm{~kg} / \mathrm{m}^{3}$ at the rate of $0.35 \mathrm{~cm} / \mathrm{s}$. The co-efficient of viscosity of the solution (neglect d
A water spray gun is attached to a hose of cross sectional area $30 \mathrm{~cm}^2$. The gun comprises of 10 perforations each of cross sectional area of $15 \mathrm{~mm}^2$. If the water flows in the hose with the speed of $50 \m
Eight mercury drops, each of radius $r$, coalesce to form a bigger drop. The surface energy released in this process is $\_\_\_\_$ - ( $S$ is the surface tension of mercury).
A liquid of density $600 \mathrm{~kg} / \mathrm{m}^3$ flowing steadily in a tube of varying cross-section. The cross-section at a point $A$ is $1.0 \mathrm{~cm}^2$ and that at $B$ is $20 \mathrm{~mm}^2$. Both the points $A$ and $B
A cylindrical vessel of 40 cm radius is completely filled with water and its capacity is $528 \mathrm{dm}^3$ (dm : decimeter) The vessel is placed on a solid block of exactly same height as vessel. If a small hole is made at 70 cm
A spherical liquid drop of radius $R$ acquires the terminal velocity $v_1$ when falls through a gas of viscosity $\eta$. Now the drop is broken into 64 identical droplets and each droplet acquires terminal velocity $v_2$ falling t
A liquid drop of diameter 2 mm breaks into 512 droplets. The change in surface energy is $\alpha \times 10^{-6}$ J. The value of $\alpha$ is _______. (Take surface tension of liquid = 0.08 N/m)
The surface tension of a soap solution is $3.5 \times 10^{-2} \mathrm{~N} / \mathrm{m}$. The work required to increase the radius of a soap bubble from 1 cm to 2 cm is $\alpha \times 10^{-6} \mathrm{~J}$. The value of $\alpha$ is
A tub is filled with water and a wooden cube $10\ \text{cm} \times 10\ \text{cm} \times 10\ \text{cm}$ is placed in the water. The wooden cube is found to float on the water with a part of it submerged in water. When a metal coin
Two ions of masses 4 amu and 16 amu have charges +2e and +3e respectively. These ions pass through the region of constant perpendicular magnetic field. The kinetic energy of both ions is same. Then :
A coil having N turns is wound tightly in the form of a spiral with inner and outer radii 'a' and 'b' respectively. Find the magnetic field at centre, when a current I passes through coil:
Two long straight wires P and Q carrying equal current 10A each were kept parallel to each other at 5 cm distance. Magnitude of magnetic force experienced by 10 cm length of wire P is F$_1$. If distance between wires is halved and
A circular loop of radius $r$ is carrying current I A. The ratio of magnetic field at the center of circular loop and at a distance r from the center of the loop on its axis is :
The electric current in a circular coil of four turns produces a magnetic induction 32 T at its centre. The coil is unwound and is rewound into a circular coil of single turn, the magnetic induction at the centre of the coil by th
A rod with circular cross-section area $2 \mathrm{~cm}^{2}$ and length $40 \mathrm{~cm}$ is wound uniformly with 400 turns of an insulated wire. If a current of $0.4 \mathrm{~A}$ flows in the wire windings, the total magnetic flux
A single turn current loop in the shape of a right angle triangle with sides 5 cm, 12 cm, 13 cm is carrying a current of 2 A. The loop is in a uniform magnetic field of magnitude 0.75 T whose direction is parallel to the current i
For a moving coil galvanometer, the deflection in the coil is 0.05 rad when a current of 10 mA is passes through it. If the torsional constant of suspension wire is $4.0\times10^{-5}\mathrm{N~m~rad^{-1}}$, the magnetic field is 0.
The magnetic moments associated with two closely wound circular coils $\mathrm{A}$ and $\mathrm{B}$ of radius $\mathrm{r}_{\mathrm{A}}=10 \mathrm{cm}$ and $\mathrm{r}_{\mathrm{B}}=20 \mathrm{~cm}$ respectively are equal if : (Wher
A long conducting wire having a current I flowing through it, is bent into a circular coil of $\mathrm{N}$ turns. Then it is bent into a circular coil of $\mathrm{n}$ turns. The magnetic field is calculated at the centre of coils
A long solenoid is formed by winding 70 turns cm$^{-1}$. If 2.0 A current flows, then the magnetic field produced inside the solenoid is ____________ ($\mu_0=4\pi\times10^{-7}$ TmA$^{-1}$)
A particle of mass $m$ and charge $q$, moving with velocity $V$ enters Region II normal to the boundary. Region II has a uniform magnetic field $B$ perpendicular to the plane of the paper. The length of the Region II is $\ell$. Re
STATEMENT-1: The sensitivity of a moving coil galvanometer is increased by placing a suitable magnetic material as a core inside the coil. and STATEMENT-2: Soft iron has a high magnetic permeability and cannot be easily magnetized
A steady current $I$ goes through a wire loop PQR having shape of a right angle triangle with PQ $= 3x$, PR $= 4x$ and QR $= 5x$. If the magnitude of the magnetic field at P due to this loop is $k\left(\dfrac{\mu_0 I}{48\pi x}\rig
A thin flexible wire of length $L$ is connected to two adjacent fixed points and carries a current $I$ in the clockwise direction, as shown in the figure. When the system is put in a uniform magnetic field of strength $B$ going in
A long insulated copper wire is closely wound as a spiral of $N$ turns. The spiral has inner radius $a$ and outer radius $b$. The spiral lies in the X-Y plane and a steady current $I$ flows through the wire. The Z-component of the
Consider the motion of a positive point charge in a region where there are simultaneous uniform electric and magnetic fields $\vec{E}=E_0\hat{j}$ and $\vec{B}=B_0\hat{j}$. At time $t=0$, this charge has velocity $\vec{v}$ in the $
A particle of mass $M$ and positive charge $Q$, moving with a constant velocity $\vec{u}_1=4\hat{i}\ \text{m s}^{-1}$, enters a region of uniform static magnetic field normal to the $x$-$y$ plane. The region of the magnetic field
A steady current $I$ flows along an infinitely long hollow cylindrical conductor of radius $R$. This cylinder is placed coaxially inside an infinite solenoid of radius $2R$. The solenoid has $n$ turns per unit length and carries a
Two parallel wires in the plane of the paper are distance $X_0$ apart. A point charge is moving with speed $u$ between the wires in the same plane at a distance $X_1$ from one of the wires. When the wires carry current of magnitud
A circular loop of radius $a$ lies between two long parallel wires (numbered 1 and 2), all in the plane of the paper. Wire 1 is the vertical line on the left through the points $P$ (lower) and $Q$ (upper); wire 2 is the vertical l
A circular loop of radius $a$ lies between two long parallel wires (numbered 1 and 2), all in the plane of the paper. The distance of each wire from the centre of the loop is $d$. The loop and the wires are carrying the same curre
PARAGRAPH: In a thin rectangular metallic strip a constant current $I$ flows along the positive $x$-direction. The length, width and thickness of the strip are $l$, $w$ and $d$, respectively. A uniform magnetic field $\vec{B}$ is
Consider two identical galvanometers and two identical resistors with resistance $R$. If the internal resistance of the galvanometers $R_C < R/2$, which of the following statement(s) about any one of the galvanometers is(are) true
A symmetric star shaped conducting wire loop (a regular six-pointed star, as shown in the figure) is carrying a steady state current $I$. The distance between the diametrically opposite vertices of the star is $4a$. The magnitude
A uniform magnetic field $B$ exists in the region between $x = 0$ and $x = \dfrac{3R}{2}$ (region 2) pointing normally into the plane of the paper. Region 1 is $x < 0$ and region 3 is $x > \dfrac{3R}{2}$. A particle with charge $+
A moving coil galvanometer has 50 turns and each turn has an area $2 \times 10^{-4}\ \mathrm{m^2}$. The magnetic field produced by the magnet inside the galvanometer is $0.02\ \mathrm{T}$. The torsional constant of the suspension
Two infinitely long straight wires lie in the $xy$-plane along the lines $x = \pm R$. The wire located at $x = +R$ carries a constant current $I_1$ and the wire located at $x = -R$ carries a constant current $I_2$. A circular loop
A circular coil of radius $R$ and $N$ turns has negligible resistance. As shown in the schematic figure, its two ends are connected to two wires and it is hanging by those wires with its plane being vertical. The wires are connect
An $\alpha$-particle (mass 4 amu) and a singly charged sulfur ion (mass 32 amu) are initially at rest. They are accelerated through a potential $V$ and then allowed to pass into a region of uniform magnetic field which is normal t
Two concentric circular loops, one of radius $R$ and the other of radius $2R$, lie in the xy-plane with the origin as their common center, as shown in the figure. The smaller loop carries current $I_1$ in the anti-clockwise direct
An infinitely long wire, located on the $z$-axis, carries a current $I$ along the $+z$-direction and produces the magnetic field $\vec{B}$. The magnitude of the line integral $\int \vec{B}\cdot \vec{dl}$ along a straight line from
A thin stiff insulated metal wire is bent into a circular loop with its two ends extending tangentially from the same point of the loop. The wire loop has mass $m$ and radius $r$ and it is in a uniform vertical magnetic field $B_0
A conducting solid sphere of radius $R$ and mass $M$ carries a charge $Q$. The sphere is rotating about an axis passing through its center with a uniform angular speed $\omega$. The ratio of the magnitudes of the magnetic dipole m
A hollow, right circular cone of base radius $R$ and height $h$, with its tip at the origin is rotating about the $Z$-axis with an angular velocity $\omega$, as shown in the figure. The cone carries a total charge $Q$ uniformly di
List-I contains four conducting loops lying in the 𝑋𝑌 plane, as shown in the figures. The loops are rotating about 𝑍 axis passing through the point 𝑂 with time period 𝑇 in clockwise direction. The region 𝑥> 0 contains a uniform ma
A particle having charge $10^{-9}$ C moving in $x$-$y$ plane in fields of $0.4 \hat{j}$ N/C and $4 \times 10^{-3} \hat{k}$ T experiences a force of $(4 \hat{i} + 2 \hat{j}) \times 10^{-10}$ N. The velocity of the particle at that
A current carrying circular loop of radius 2 cm with unit normal $\hat{n}=\frac{\hat{k}+\hat{i}}{\sqrt{2}}$ is placed in a magnetic field, $\vec{B}=B_o(3 \hat{i}+2 \hat{k})$. If $B_o=4 \times 10^{-3} \mathrm{~T}$ and current $I=10
An insulated wire is wound so that it forms a flat coil with $N=200$ turns. The radius of the innermost turn is $r_1=3 \mathrm{~cm}$, and of the outermost turn $r_2=6 \mathrm{~cm}$. If 20 mA current flows in it then the magnetic m
A small cube of side 1 mm is placed at the centre of a circular loop of radius 10 cm carrying a current of 2 A . The magnetic energy stored inside the cube is $\alpha \times 10^{-14} \mathrm{~J}$. The value of $\alpha$ is $\_\_\_\
In a vacuum chamber, a particle of charge $1\ \mu\mathrm{C}$ and mass $1\ \mathrm{mg}$ is projected with a velocity $(\hat{i} + 2\hat{j})\ \mathrm{ms^{-1}}$ from the $XZ$ plane at time $t = 0$ in an electric field of $1\hat{i}\ \m
An electron and a proton are moving on straight parallel paths with same velocity. They enter a semi- infinite region of uniform magnetic field perpendicular to the velocity. Which of the following statement(s) is / are true?
A particle of mass M and positive charge Q, moving with a constant velocity 1 1 ˆ u 4ims , enters a region of uniform static magnetic field normal to the x-y plane. The region of the magnetic field extends from x = 0 to x = L f
A steady current I flows along an infinitely long hollow cylindrical conductor of radius R. This cylinder is placed coaxially inside an infinite solenoid of radius 2R. The solenoid has n turns per unit length and carries a steady
A charge particle of $2 ~\mu \mathrm{C}$ accelerated by a potential difference of $100 \mathrm{~V}$ enters a region of uniform magnetic field of magnitude $4 ~\mathrm{mT}$ at right angle to the direction of field. The charge parti
Two long parallel wires carrying currents 8A and 15A in opposite directions are placed at a distance of 7 cm from each other. A point P is at equidistant from both the wires such that the lines joining the point P to the wires are
A long straight wire of circular cross-section (radius a) is carrying steady current I. The current I is uniformly distributed across this cross-section. The magnetic field is
A charge particle moving in magnetic field B, has the components of velocity along B as well as perpendicular to B. The path of the charge particle will be
An electron is allowed to move with constant velocity along the axis of current carrying straight solenoid. A. The electron will experience magnetic force along the axis of the solenoid. B. The electron will not experience magneti
An electron is moving along the positive $\mathrm{x}$-axis. If the uniform magnetic field is applied parallel to the negative z-axis, then A. The electron will experience magnetic force along positive y-axis B. The electron will e
A proton with a kinetic energy of $2.0 ~\mathrm{eV}$ moves into a region of uniform magnetic field of magnitude $\frac{\pi}{2} \times 10^{-3} \mathrm{~T}$. The angle between the direction of magnetic field and velocity of proton i
The ratio of magnetic field at the centre of a current carrying coil of radius $r$ to the magnetic field at distance $r$ from the centre of coil on its axis is $\sqrt{x}: 1$. The value of $x$ is __________
A particle of charge $q$ and mass $m$ is projected from origin with an initial velocity $\vec{v}=\left(\frac{v_0}{\sqrt{2}} \hat{x}+\frac{v_0}{\sqrt{2}} \hat{y}\right)$. There exists a uniform magnetic field $\vec{B}=B_0 \hat{z}$
A current of 30 A each flows in opposite directions in two conducting wires, placed parallel to each other at a distance of 8 cm . The magnetic field at the mid point between the two wires is $\_\_\_\_ \mu \mathrm{T}$. $\left(\fra
1 $\mu$C charge moving with velocity $\vec{v} = (\hat{i} - 2\hat{j} + 3\hat{k})$ m/s in the region of magnetic field $\vec{B} = (2\hat{i} + 3\hat{j} - 5\hat{k})$ T. The magnitude of force acting on it is $\sqrt{\alpha} \times 10^{
A moving coil of galvanometer when shunted with $2 \Omega$ resistance gives a full scale deflection for a current of 500 mA . When a resistance of $470 \Omega$ is connected in series it gives a full scale deflection for 10 V poten
A 5 mg particle carrying a charge of $5 \pi \times 10^{-6} \mathrm{C}$ is moving with velocity of $(3 \hat{i}+2 \hat{k}) \times 10^{-2} \mathrm{~m} / \mathrm{s}$ in a region having magnetic field $\vec{B}=0.1 \hat{k} \mathrm{~Wb}
A circular coil of radius 2 cm and 125 turns carries a current of 1 A . The coil is placed in a uniform magnetic field of magnitude 0.4 T . The axis of the coil makes an angle of $30^{\circ}$ with the direction of the magnetic fie
The charged particle moving in a uniform magnetic field of $(3 \hat{i}+2 \hat{j}) \mathrm{T}$ has an acceleration $\left(4 \hat{i}-\frac{x}{2} \hat{j}\right) \mathrm{m} / \mathrm{s}^2$. The value of $x$ is
There are $10^{10}$ radioactive nuclei in a given radioactive element, its half-life time is 1 minute. How many nuclei will remain after 30 seconds? $\left( {\sqrt 2 = 1.414} \right)$
The half life period of radioactive element x is same as the mean life time of another radioactive element y. Initially they have the same number of atoms. Then :
Substance A has atomic mass number 16 and half life of 1 day. Another substance B has atomic mass number 32 and half life of $\frac{1}{2}$ day. If both A and B simultaneously start undergo radio activity at the same time with init
Given below are two statements: one is labelled as Assertion $\mathbf{A}$ and the other is labelled as Reason $\mathbf{R}$ Assertion A: The nuclear density of nuclides ${ }_{5}^{10} \text{~B},{ }_{3}^{6} \text{Li},{ }_{26}^{56} \t
A free neutron decays into a proton but a free proton does not decay into neutron. This is because
The ratio of the density of oxygen nucleus ($_8^{16}O$) and helium nucleus ($_2^{4}\text{He}$) is
The mass of proton, neutron and helium nucleus are respectively $1.0073~u,1.0087~u$ and $4.0015~u$. The binding energy of helium nucleus is :
If a radioactive element having half-life of $30 \text{~min}$ is undergoing beta decay, the fraction of radioactive element remains undecayed after $90 \text{~min}$. will be
The energy released per fission of nucleus of $^{240}$X is 200 MeV. The energy released if all the atoms in 120g of pure $^{240}$X undergo fission is ____________ $\times$ 10$^{25}$ MeV. (Given $\text{N_A=6\times10^{23}}$)
A nucleus disintegrates into two smaller parts, which have their velocities in the ratio 3 : 2. The ratio of their nuclear sizes will be ${\left( {{x \over 3}} \right)^{{1 \over 3}}}$. The value of '$x$' is :-
Two radioactive substances A and B of mass numbers 200 and 212 respectively, shows spontaneous $\alpha$-decay with same $Q$ value of 1 MeV . The ratio of energies of $\alpha$-rays produced by A and B is $\_\_\_\_$ .
A radioactive element $_{92}^{242}$X emits two $\alpha$-particles, one electron and two positrons. The product nucleus is represented by $_{\text{P}}^{234}$Y. The value of P is __________.
A radioactive nucleus decays by two different process. The half life of the first process is 5 minutes and that of the second process is $30 \text{~s}$. The effective half-life of the nucleus is calculated to be $\frac{\alpha}{11}
Assume that protons and neutrons have equal masses. Mass of a nucleon is $1.6\times10^{-27}$ kg and radius of nucleus is $1.5\times10^{-15}~\text{A^{1/3}}$ m. The approximate ratio of the nuclear density and water density is $n\ti
Two radioactive elements A and B initially have same number of atoms. The half life of A is same as the average life of B. If $\lambda_{A}$ and $\lambda_{B}$ are decay constants of A and B respectively, then choose the correct rel
The half-life of a radioactive nucleus is 5 years. The fraction of the original sample that would decay in 15 years is:
Given below are two statements: one is labelled as Assertion $\mathbf{A}$ and the other is labelled as Reason $\mathbf{R}$ Assertion A : The binding energy per nucleon is practically independent of the atomic number for nuclei of
For a nucleus ${ }_{\text{A}}^{\text{A}} \text{X}$ having mass number $\text{A}$ and atomic number $\text{Z}$ A. The surface energy per nucleon $\left(b_{\text{s}}\right)=-a_{1} A^{2 / 3}$. B. The Coulomb contribution to the bindi
The half life of a radioactive substance is T. The time taken, for disintegrating $\frac{7}{8}$th part of its original mass will be:
A radio active material is reduced to $1 / 8$ of its original amount in 3 days. If $8 \times 10^{-3} \text{~kg}$ of the material is left after 5 days the initial amount of the material is
A nucleus with mass number 242 and binding energy per nucleon as $7.6~ \text{MeV}$ breaks into two fragment each with mass number 121. If each fragment nucleus has binding energy per nucleon as $8.1 ~\text{MeV}$, the total gain in
A nucleus disintegrates into two nuclear parts, in such a way that ratio of their nuclear sizes is $1: 2^{1 / 3}$. Their respective speed have a ratio of $n: 1$. The value of $n$ is __________.
The decay constant for a radioactive nuclide is 1.5 $\times$ 10$^{-5}$ s$^{-1}$. Atomic weight of the substance is 60 g mole$^{-1}$, ($N_A=6\times10^{23}$). The activity of 1.0 $\mu$g of the substance is ___________ $\times$ 10$^{
Two nuclei of mass number 3 combine with another nucleus of mass number 4 to yield a nucleus of mass number 10. If the binding energy per nucleon for the mass numbers 3,4 and 10 are $5.6 \text{MeV}, 7.4 \text{MeV}$ and 6.1 MeV , r
Assuming the experimental mass of ${ }_6^{12} C$ as $12 u$, the mass defect of ${ }_6^{12} C$ atom is $\_\_\_\_ \text{MeV} / \text{c}^2$. (Mass of proton $=1.00727 \text{u}$. mass of neutron $=1.00866 \text{u}, 1 \text{u}=931.5 \t
An object is placed at the focus of concave lens having focal length f. What is the magnification and distance of the image from the optical centre of the lens?
An object is placed beyond the centre of curvature C of the given concave mirror. If the distance of the object is $d_{1}$ from C and the distance of the image formed is $d_{2}$ from C, the radius of curvature of this mirror is :
A glass tumbler having inner depth of 17.5 cm is kept on a table. A student starts pouring water ($\mu$ = 4/3) into it while looking at the surface of water from the above. When he feels that the tumbler is half filled, he stops p
The light rays from an object have been reflected towards an observer from a standard flat mirror, the image observed by the observer are :- A. Real B. Erect C. Smaller in size then object D. Laterally inverted Choose the most app
A person has been using spectacles of power $-1.0$ dioptre for distant vision and a separate reading glass of power $2.0$ dioptres. What is the least distance of distinct vision for this person :
A microscope is focused on an object at the bottom of a bucket. If liquid with refractive index $\frac{5}{3}$ is poured inside the bucket, then the microscope has to be raised by $30 \mathrm{~cm}$ to focus the object again. The he
A thin prism $P_1$ with an angle $6^{\circ}$ and made of glass of refractive index $1.54$ is combined with another prism $P_2$ made from glass of refractive index $1.72$ to produce dispersion without average deviation. The angle o
When a beam of white light is allowed to pass through convex lens parallel to principal axis, the different colours of light converge at different point on the principle axis after refraction. This is called :
A scientist is observing a bacteria through a compound microscope. For better analysis and to improve its resolving power he should. (Select the best option)
In an experiment of measuring the refractive index of a glass slab using travelling microscope in physics lab, a student measures real thickness of the glass slab as 5.25 mm and apparent thickness of the glass slab as 5.00 mm. Tra
A thin cylindrical rod of length $10 \mathrm{~cm}$ is placed horizontally on the principle axis of a concave mirror of focal length $20 \mathrm{~cm}$. The rod is placed in a such a way that mid point of the rod is at $40 \mathrm{~
A convex lens of refractive index 1.5 and focal length 18cm in air is immersed in water. The change in focal length of the lens will be ___________ cm. (Given refractive index of water $=\frac{4}{3}$)
In an experiment for estimating the value of focal length of converging mirror, image of an object placed at $40 \mathrm{~cm}$ from the pole of the mirror is formed at distance $120 \mathrm{~cm}$ from the pole of the mirror. These
Given below are two statements: one is labelled as Assertion A and the other is labelled as Reason R Assertion A: The phase difference of two light waves change if they travel through different media having same thickness, but dif
A 2 meter long scale with least count of $0.2 \mathrm{~cm}$ is used to measure the locations of objects on an optical bench. While measuring the focal length of a convex lens, the object pin and the convex lens are placed at $80 \
A monochromatic light wave with wavelength $\lambda_{1}$ and frequency $v_{1}$ in air enters another medium. If the angle of incidence and angle of refraction at the interface are $45^{\circ}$ and $30^{\circ}$ respectively, then t
An object is placed at a distance of 12 cm in front of a plane mirror. The virtual and erect image is formed by the mirror. Now the mirror is moved by 4 cm towards the stationary object. The distance by which the position of image
When one light ray is reflected from a plane mirror with $30^{\circ}$ angle of reflection, the angle of deviation of the ray after reflection is :
A vessel of depth '$d$' is half filled with oil of refractive index $n_{1}$ and the other half is filled with water of refractive index $n_{2}$. The apparent depth of this vessel when viewed from above will be-
In a reflecting telescope, a secondary mirror is used to:
The radius of curvature of each surface of a convex lens having refractive index 1.8 is $20 \mathrm{~cm}$. The lens is now immersed in a liquid of refractive index 1.5 . The ratio of power of lens in air to its power in the liquid
A fish rising vertically upward with a uniform velocity of $8 \mathrm{~ms}^{-1}$, observes that a bird is diving vertically downward towards the fish with the velocity of $12 \mathrm{~ms}^{-1}$. If the refractive index of water is
A bi convex lens of focal length $10 \mathrm{~cm}$ is cut in two identical parts along a plane perpendicular to the principal axis. The power of each lens after cut is ____________ D.
Two transparent media having refractive indices 1.0 and 1.5 are separated by a spherical refracting surface of radius of curvature $30 \mathrm{~cm}$. The centre of curvature of surface is towards denser medium and a point object i
A pole is vertically submerged in swimming pool, such that it gives a length of shadow $2.15 \mathrm{~m}$ within water when sunlight is incident at angle of $30^{\circ}$ with the surface of water. If swimming pool is filled to a h
A thin biconvex lens is prepared from the glass $(\mu=1.5)$ both curved surfaces of which have equal radii of 20 cm each. Left side surface of the lens is silvered from outside to make it reflecting. To have the position of image
For a thin symmetric prism made of glass (refractive index 1.5), the ratio of incident angle and minimum deviation will be _______.
A ray of light passing through an equilateral prism is having velocity $2.12 \times 10^8 \mathrm{~m} / \mathrm{s}$ in the prism material, then the minimum angle of deviation is $\_\_\_\_$ degrees.
A thin convex lens and a thin concave lens are kept in contact and are co-axial. Which of the following statements is correct for this combination of two lenses ?
A convex lens is made from glass material having refractive index of 1.4 with same radius of curvature on both sides. The ratio of its focal length and radius of curvature is $\_\_\_\_$ .
A compound microscope is designed with two symmetric biconvex lenses. The objective lens is cut vertically, creating two identical plano-convex lenses. One of them is used in place of original objective lens. To retain same magnif
Angle of minimum deviation is equal to the half of the angle of prism in an equilateral prism. The refractive index of the prism is $\_\_\_\_$
A telescope with objective diameter $R$ is used to observe a distant star emitting light of wavelength 500 nm , at a resolution of $5 \times 10^{-7}$ radian. The value of $R$ is $\_\_\_\_$ cm .
Some distant star is to be observed by some telescope of diameter of objective lens $a$, at an angular resolution of $3.0 \times 10^{-7}$ radian. If the wavelength of light from the star reaching the telescope is 500 nm , the mini
If sunlight is focused on a paper using convex lens, it starts burning the paper in shortest time when the lens is kept at 30 cm above the paper. If the radius of curvature of the lens is 60 cm then the refractive index of the len
A concave mirror of focal length 10 cm forms an image which is double the size of object when the object is placed at two different positions. The distance between the two positions of the object is $\_\_\_\_$ cm.
A system consists of two identical spheres each of mass 1.5 kg and radius 50 cm at the end of light rod. The distance between the centres of the two spheres is 5 m. What will be the moment of inertia of the system about an axis pe
Moment of inertia of a square plate of side l about the axis passing through one of the corner and perpendicular to the plane of square plate is given by :
Angular momentum of a single particle moving with constant speed along circular path :
A uniform solid cylinder with radius R and length L has moment of inertia I$_1$, about the axis of the cylinder. A concentric solid cylinder of radius $R'=\frac{R}{2}$ and length $L'=\frac{L}{2}$ is carved out of the original cyli
A solid sphere of mass 2 kg is making pure rolling on a horizontal surface with kinetic energy 2240 J. The velocity of centre of mass of the sphere will be _______ ms$^{-1}$.
A solid sphere of mass $1 \mathrm{~kg}$ rolls without slipping on a plane surface. Its kinetic energy is $7 \times 10^{-3} \mathrm{~J}$. The speed of the centre of mass of the sphere is __________ $\operatorname{cm~s}^{-1}$
Two discs of same mass and different radii are made of different materials such that their thicknesses are $1 \mathrm{~cm}$ and $0.5 \mathrm{~cm}$ respectively. The densities of materials are in the ratio $3: 5$. The moment of ine
If a solid sphere of mass 5 kg and a disc of mass 4 kg have the same radius. Then the ratio of moment of inertia of the disc about a tangent in its plane to the moment of inertia of the sphere about its tangent will be $\frac{x}{7
A thin uniform rod of length $2 \mathrm{~m}$, cross sectional area '$A$' and density '$\mathrm{d}$' is rotated about an axis passing through the centre and perpendicular to its length with angular velocity $\omega$. If value of $\
Given below are two statements: one is labelled as Assertion $\mathbf{A}$ and the other is labelled as Reason $\mathbf{R}$ Assertion A : An electric fan continues to rotate for some time after the current is switched off. Reason R
A solid sphere is rolling on a horizontal plane without slipping. If the ratio of angular momentum about axis of rotation of the sphere to the total energy of moving sphere is $\pi: 22$ then, the value of its angular speed will be
A light rope is wound around a hollow cylinder of mass 5 kg and radius 70 cm. The rope is pulled with a force of 52.5 N. The angular acceleration of the cylinder will be _________ rad s$^{-2}$.
The moment of inertia of a semicircular ring about an axis, passing through the center and perpendicular to the plane of ring, is $\frac{1}{x} \mathrm{MR}^{2}$, where $\mathrm{R}$ is the radius and $M$ is the mass of the semicircu
A circular plate is rotating in horizontal plane, about an axis passing through its center and perpendicular to the plate, with an angular velocity $\omega$. A person sits at the center having two dumbbells in his hands. When he s
A solid sphere of mass $500 \mathrm{~g}$ and radius $5 \mathrm{~cm}$ is rotated about one of its diameter with angular speed of $10 ~\mathrm{rad} ~\mathrm{s}^{-1}$. If the moment of inertia of the sphere about its tangent is $x \t
A solid sphere and a solid cylinder of same mass and radius are rolling on a horizontal surface without slipping. The ratio of their radius of gyrations respectively $\left(k_{\text {sph }}: k_{\text {cyl }}\right)$ is $2: \sqrt{x
Two identical solid spheres each of mass $2 \mathrm{~kg}$ and radii $10 \mathrm{~cm}$ are fixed at the ends of a light rod. The separation between the centres of the spheres is $40 \mathrm{~cm}$. The moment of inertia of the syste
A ring and a solid sphere rotating about an axis passing through their centers have same radii of gyration. The axis of rotation is perpendicular to plane of ring. The ratio of radius of ring to that of sphere is $\sqrt{\frac{2}{x
A solid sphere $(A)$ of mass $5 m$ and a spherical shell $(B)$ of mass $m$, both having same radius, are placed on a rough surface. When a force of same magnitude is applied tangentially at the highest points of $A$ and $B$, they
The position of an object having mass 0.1 kg as a function of time $t$ is given as $\vec{r} = \left( 10 t^2 \hat{i} + 5 t^3 \hat{j} \right)$ m. At $t = 1$ s, which of the following statements are correct ? A. The linear momentum $
A wheel initially at rest is subjected to a uniform angular acceleration about its axis. In the first 2 s it rotates through an angle $\theta_1$ and in the next 2 s it rotates through an angle $\theta_2$. The ratio $\frac{\theta_2
A solid sphere of radius 4 cm and mass 5 kg is rotating (rotation axis is passing through the centre of the sphere) with an angular velocity of 1200 rpm . It is brought to rest in 10 s by applying a constant torque. The torque app
Two identical bodies A and B of equal masses have initial velocities $\overrightarrow{v_1}=4 \hat{i} \mathrm{~m} / \mathrm{s}$ and $\overrightarrow{v_2}=4 \hat{j} \mathrm{~m} / \mathrm{s}$ respectively. The body A has acceleration
A solid cylinder having radius $R$ and length $L$ is slipping on a rough horizontal plane. At time $t=0$ the cylinder has a translational velocity $v_{\mathrm{o}}=49 \mathrm{~m} / \mathrm{s}$, perpendicular to its axis and a rotat
A source supplies heat to a system at the rate of $1000 \mathrm{~W}$. If the system performs work at a rate of $200 \mathrm{~W}$. The rate at which internal energy of the system increases is
Work done by a Carnot engine operating between temperatures $127^{\circ} \mathrm{C}$ and $27^{\circ} \mathrm{C}$ is $2 \mathrm{~kJ}$. The amount of heat transferred to the engine by the reservoir is :
Consider two containers A and B containing monoatomic gases at the same Pressure (P), Volume (V) and Temperature (T). The gas in A is compressed isothermally to $\frac{1}{8}$ of its original volume while the gas in B is compressed
The Thermodynamic process, in which internal energy of the system remains constant is
A gas is compressed adiabatically, which one of the following statement is NOT true.
Given below are two statements: Statement I: If heat is added to a system, its temperature must increase. Statement II: If positive work is done by a system in a thermodynamic process, its volume must increase. In the light of the
A cylinder with adiabatic walls is closed at both ends and is divided into two compartments by a frictionless adiabatic piston. Ideal gas is filled in both (left and right) the compartments at same $P, V$, T. Heating is started fr
Heat is supplied to a diatomic gas at constant pressure. Then the ratio of $\Delta Q : \Delta U : \Delta W$ is ______.
An ideal gas at pressure $P$ and temperature $T$ is expanding such that $P T^3=$ constant. The coefficient of volume expansion of the gas is $\_\_\_\_$ .
One mole of diatomic gas having rotational modes only is kept in a cylinder with a piston system. The cross-section area of the cylinder is $4 \mathrm{~cm}^2$. The gas is heated slowly to raise the temperature by $1.2^{\circ} \mat
An ideal gas undergoes a process maintaining relation between pressure $(P)$ and $\operatorname{volume}(V)$ as $P=P_{\mathrm{o}}\left(1+\left(\frac{V_{\mathrm{o}}}{V}\right)^2\right)^{-1}$, where $P_{\mathrm{o}}$ and $V_{\mathrm{o
A vessel contains 0.15 $m^{3}$ of a gas at pressure 8 bar and temperature 140 °C with $c_p = 3R$ and $c_v = 2R$. It is expanded adiabatically till pressure falls to 1 bar. The work done during this process is _________ kJ. (R is g
5 moles of unknown gas is heated at constant volume from 10°C to 20°C. The molar specific heat of this gas at constant pressure $c_p = 8$ cal/mol.°C and $R = 8.36$ J/mol.°C. The change in the internal energy of the gas is ________
In the determination of Young’s modulus 2 4MLg Y d = π l by using Searle’s method, a wire of length L = 2m and diameter d = 0.5 mm is used. For a load M = 2.5 kg, an extension l = 0.25 mm in the length of the wire is o
In an experiment to determine the acceleration due to gravity g, the formula used for the time period of a periodic motion is 7 R r T 2 5g ( ) . The values of R and r are measured to be (60 1) mm and (10 1) mm, respective
Let us consider a system of units in which mass and angular momentum are dimensionless. If length has dimension of L, which of the following statement(s) is/are correct?
One main scale division of a vernier callipers is 'a' cm and $n^{th}$ division of the vernier scale coincide with (n $- 1)^{th}$ division of the main scale. The least count of the callipers in mm is :
If E and H represents the intensity of electric field and magnetising field respectively, then the unit of E/H will be :
In a Screw Gauge, fifth division of the circular scale coincides with the reference line when the ratchet is closed. There are 50 divisions on the circular scale, and the main scale moves by 0.5 mm on a complete rotation. For a pa
If the length of the pendulum in pendulum clock increases by 0.1%, then the error in time per day is :
Assertion A : If in five complete rotations of the circular scale, the distance travelled on main scale of the screw gauge is 5 mm and there are 50 total divisions on circular scale, then least count is 0.001 cm. Reason R : Least
In a screw gauge, there are 100 divisions on the circular scale and the main scale moves by $0.5 \mathrm{~mm}$ on a complete rotation of the circular scale. The zero of circular scale lies 6 divisions below the line of graduation
A cylindrical wire of mass $(0.4 \pm 0.01) \mathrm{g}$ has length $(8 \pm 0.04) \mathrm{cm}$ and radius $(6 \pm 0.03) \mathrm{mm}$. The maximum error in its density will be:
In an experiment with vernier callipers of least count $0.1 \mathrm{~mm}$, when two jaws are joined together the zero of vernier scale lies right to the zero of the main scale and 6th division of vernier scale coincides with the m
Two resistances are given as $\mathrm{R}_{1}=(10 \pm 0.5) \Omega$ and $\mathrm{R}_{2}=(15 \pm 0.5) \Omega$. The percentage error in the measurement of equivalent resistance when they are connected in parallel is -
If force (F), velocity (V) and time (T) are considered as fundamental physical quantity, then dimensional formula of density will be :
The speed of a wave produced in water is given by $v=\lambda^{a} g^{b} \rho^{c}$. Where $\lambda, g$ and $\rho$ are wavelength of wave, acceleration due to gravity and density of water respectively. The values of $a, b$ and $c$ re
Given below are two statements : Statements I : Astronomical unit (Au), Parsec (Pc) and Light year (ly) are units for measuring astronomical distances. Statements II : $\mathrm{Au} < \mathrm{Parsec} (\mathrm{Pc}) < \mathrm{ly}$ In
A body of mass $(5 \pm 0.5) ~\mathrm{kg}$ is moving with a velocity of $(20 \pm 0.4) ~\mathrm{m} / \mathrm{s}$. Its kinetic energy will be
While measuring diameter of wire using screw gauge the following readings were noted. Main scale reading is $1 \mathrm{~mm}$ and circular scale reading is equal to 42 divisions. Pitch of screw gauge is $1 \mathrm{~mm}$ and it has
The dimensional formula of $\frac{1}{2} \epsilon_0 E^2$ ($\epsilon_0$ = permittivity of vacuum and $E$ = electric field) is $M^a L^b T^c$. The value of $2a - b + c =$ ________.
Dimensions of universal gravitational constant ($G$) in terms of Planck's constant ($h$), distance ($L$), mass ($M$) and time ($T$) are _______.
In a screw gauge when the circular scale is given five complete rotations it moves linearly by 2.5 mm . If the circular scale has 100 divisions, the least count of screw gauge is $\_\_\_\_$ mm.
In a Vernier calipers, when both jaws touch each other, zero of the Vernier scale is shifted to the right of zero of the main scale and $7^{\text {th }}$ Vernier division coincides with a main scale reading. If the value of 1 main
The density $\rho$ of a uniform cylinder is determined by measuring its mass $m$, length $l$ and diameter $d$. The measured values of $m, l$ and $d$ are $97.42 \pm 0.02 \mathrm{~g}$, $8.35 \pm 0.05 \mathrm{~mm}$ and $20.20 \pm 0.0
A new unit ( $\alpha$ ) of length is chosen such that it is equal to the speed of light in vacuum. What is the distance between Venus and Earth in terms of $\alpha$ units if light takes 6 min. 40 s to cover this distance?
$L, C$ and $R$ represents physical quantities inductance, capacitance and resistance respectively. The dimensional formula $\mathrm{ML}^2 \mathrm{~T}^{-4} \mathrm{~A}^{-2}$ corresponds to $\_\_\_\_$ .
The potential energy of a particle changes with distance $x$ from a fixed origin as $V=\frac{A \sqrt{x}}{x+B}$, where $A$ and $B$ are constant with appropriate dimensions. The dimensions of $A B$ are $\_\_\_\_$
Consider the equation $H=\frac{x^p \epsilon^q E^r}{t^s}$ Where $H=$ magnetic field; $E=$ electric field, $\epsilon=$ permittivity, $x=$ distance, $t=$ time The values of $p, q, r$ and $s$ respectively are :
In a screw gauge the zero of main scale reference line coincides with the fifth division of the circular scale when two studs are in contact. There are 100 divisions in circular scale and pitch of screw gauge is 0.1 mm. When diame
Equation of travelling wave on a stretched string of linear density 5 g/m is y = 0.03 sin(450 t – 9x) where distance and time are measured in SI units. The tension in the string is :
A stationary observer receives sound from two identical tuning forks, one of which approaches and the other one recedes with the same speed (much less than the speed of sound). The observer hears 2 beats/sec. The oscillation frequ
In a resonance tube experiment when the tube is filled with water up to a height of 17.0 cm from bottom, it resonates with a given tuning fork. When the water level is raised the next resonance with the same tuning fork occurs at
A driver in a car, approaching a vertical wall notices that the frequency of his car horn, has changed from 440 Hz to 480 Hz, when it gets reflected from the wall. If the speed of sound in air is 345 m/s, then the speed of the car
Speed of a transverse wave on a straight wire (mass 6.0 g, length 60 cm and area of cross-section 1.0 $mm^{2}$) is 90 $ms^{-1}$. If the Young's modulus of wire is 16 $\times 10^{11} Nm^{-2}$, the extension of wire over its natural
A uniform thin rope of length 12 m and mass 6 kg hangs vertically from a rigid support and a block of mass 2 kg is attached to its free end. A transverse short wavetrain of wavelength 6 cm is produced at the lower end of the rope.
A transverse wave travels on a taut steel wire with a velocity of v when tension in it is 2.06 × $10^{4}$ N. When the tension is changed to T, the velocity changed to v/2. The value of T is close to :
Assume that the displacement(s) of air is proportional to the pressure difference ($\Delta$p) created by a sound wave. Displacement (s) further depends on the speed of sound (v), density of air ($\rho$) and the frequency (f). If $
The equations of two waves are given by : $y_{1}$ = 5 sin 2$\pi$(x - vt) cm $y_{2}$ = 3 sin 2$\pi$(x $-$ vt + 1.5) cm These waves are simultaneously passing through a string. The amplitude of the resulting wave is :
A transverse wave is represented by $y=2 \sin (\omega t-k x)\, \mathrm{cm}$. The value of wavelength (in $\mathrm{cm}$) for which the wave velocity becomes equal to the maximum particle velocity, will be :
An observer moves towards a stationary source of sound with a velocity equal to one-fifth of the velocity of sound. The percentage change in the frequency will be :
If a wave gets refracted into a denser medium, then which of the following is true?
A train blowing a whistle of frequency 320 Hz approaches an observer standing on the platform at a speed of 66 m/s. The frequency observed by the observer will be (given speed of sound = 330 ms$^{-1}$) __________ Hz.
Two simple harmonic waves having equal amplitudes of 8 cm and equal frequency of 10 Hz are moving along the same direction. The resultant amplitude is also 8 cm. The phase difference between the individual waves is _________ degre
The distance between two consecutive points with phase difference of 60$^\circ$ in a wave of frequency 500 Hz is 6.0 m. The velocity with which wave is travelling is __________ km/s
The engine of a train moving with speed $10 \mathrm{~ms}^{-1}$ towards a platform sounds a whistle at frequency $400 \mathrm{~Hz}$. The frequency heard by a passenger inside the train is: (neglect air speed. Speed of sound in air
A car P travelling at $20 \mathrm{~ms}^{-1}$ sounds its horn at a frequency of $400 \mathrm{~Hz}$. Another car $\mathrm{Q}$ is travelling behind the first car in the same direction with a velocity $40 \mathrm{~ms}^{-1}$. The frequ
In an experiment with sonometer when a mass of $180 \mathrm{~g}$ is attached to the string, it vibrates with fundamental frequency of $30 \mathrm{~Hz}$. When a mass $\mathrm{m}$ is attached, the string vibrates with fundamental fr
A transverse harmonic wave on a string is given by $y(x,t) = 5\sin (6t + 0.003x)$ where x and y are in cm and t in sec. The wave velocity is _______________ ms$^{-1}$.
An organ pipe $40 \mathrm{~cm}$ long is open at both ends. The speed of sound in air is $360 \mathrm{~ms}^{-1}$. The frequency of the second harmonic is ___________ $\mathrm{Hz}$.
The fundamental frequency of vibration of a string stretched between two rigid support is $50 \mathrm{~Hz}$. The mass of the string is $18 \mathrm{~g}$ and its linear mass density is $20 \mathrm{~g} / \mathrm{m}$. The speed of the
The equation of wave is given by $\mathrm{Y}=10^{-2} \sin 2 \pi(160 t-0.5 x+\pi / 4)$ where $x$ and $Y$ are in $\mathrm{m}$ and $\mathrm{t}$ in $s$. The speed of the wave is ________ $\mathrm{km} ~\mathrm{h}^{-1}$.
A person driving car at a constant speed of $15 \mathrm{~m} / \mathrm{s}$ is approaching a vertical wall. The person notices a change of $40 \mathrm{~Hz}$ in the frequency of his car's horn upon reflection from the wall. The frequ
A guitar string of length 90 cm vibrates with a fundamental frequency of 120 Hz. The length of the string producing a fundamental frequency of 180 Hz will be _________ cm.
The fundamental frequency of a closed organ pipe is equal to the first overtone frequency of an open organ pipe. If length of the open pipe is $60 \mathrm{~cm}$, the length of the closed pipe will be:
The equation of a plane progressive wave is given by $y = 5 \cos \pi \left( 200t - \frac{x}{150} \right)$ where $x$ and $y$ are in cm and $t$ is in second. The velocity of the wave is ________ m/s.
A transverse wave on a string is described by $y=3 \sin (36 t+0.018 x+\pi / 4)$. where $x, y$ are in cm and $t$ in seconds. The least distance between the two successive crests in the wave is $\_\_\_\_$ cm . (Nearest integer) $(\p
A particle of mass M is moving in a circle of fixed radius R in such a way that its centripetal acceleration at time t is given by $n^{2}$ R $t^{2}$ where n is a constant. The power delivered to the particle by the force acting on
An object is dropped from a height h from the ground. Every time it hits the ground it looses 50% of its kinetic energy. The total distance covered as t $\to \infty$ is :
A 60 HP electric motor lifts an elevator having a maximum total load capacity of 2000 kg. If the frictional force on the elevator is 4000 N, the speed of the elevator at full load is close to : (1 HP = 746 W, g = 10 $ms^{-2}$)
A block moving horizontally on a smooth surface with a speed of 40 m/s splits into two parts with masses in the ratio of 1 : 2. If the smaller part moves at 60 m/s in the same direction, then the fractional change in kinetic energ
A body of mass $0.5 \mathrm{~kg}$ travels on straight line path with velocity $v=\left(3 x^{2}+4\right) \mathrm{m} / \mathrm{s}$. The net workdone by the force during its displacement from $x=0$ to $x=2 \mathrm{~m}$ is :
A stone is projected at angle $30^{\circ}$ to the horizontal. The ratio of kinetic energy of the stone at point of projection to its kinetic energy at the highest point of flight will be -
If a rubber ball falls from a height $h$ and rebounds upto the height of $h / 2$. The percentage loss of total energy of the initial system as well as velocity ball before it strikes the ground, respectively, are :
A spherical ball of mass 2 kg falls from a height of 10 m and is brought to rest after penetrating 10 cm into sand. The average force exerted by sand on the ball is _________ N. (Take $g = 10 \ \mathrm{m/s^2}$)
An elevator in a building can carry a maximum of 10 persons, with the average mass of each person being 68 kg, The mass of the elevator itself is 920 kg and it moves with a constant speed of 3 m/s. The frictional force opposing th
A body at rest is moved along a horizontal straight line by a machine delivering a constant power. The distance moved by the body in time 't' is proportional to :
A body of mass 'm' dropped from a height 'h' reaches the ground with a speed of 0.8$\sqrt {gh}$. The value of workdone by the air-friction is :
An automobile of mass 'm' accelerates starting from origin and initially at rest, while the engine supplies constant power P. The position is given as a function of time by :
Identify the correct statements from the following : A. Work done by a man in lifting a bucket out of a well by means of a rope tied to the bucket is negative. B. Work done by gravitational force in lifting a bucket out of a well
A constant power delivering machine has towed a box, which was initially at rest, along a horizontal straight line. The distance moved by the box in time 't' is proportional to :-
A lift of mass $\mathrm{M}=500 \mathrm{~kg}$ is descending with speed of $2 \mathrm{~ms}^{-1}$. Its supporting cable begins to slip thus allowing it to fall with a constant acceleration of $2 \mathrm{~ms}^{-2}$. The kinetic energy
Sand is being dropped from a stationary dropper at a rate of $0.5 \,\mathrm{kgs}^{-1}$ on a conveyor belt moving with a velocity of $5 \mathrm{~ms}^{-1}$. The power needed to keep the belt moving with the same velocity will be :
When a rubber-band is stretched by a distance $x$, it exerts restoring force of magnitude $F = ax + b{x^2}$ where $a$ and $b$ are constants. The work done in stretching the unstretched rubber-band by $L$ is :
A person trying to lose weight by burning fat lifts a mass of $10 kg$ upto a height of $1 m 1000$ times. Assume that the potential energy lost each time he lowers the mass is dissipated. How much fat will he use up considering the
A body of mass 1 kg collides head on elastically with a stationary body of mass 3 kg. After collision, the smaller body reverses its direction of motion and moves with a speed of 2 m/s. The initial speed of the smaller body before
The ratio of powers of two motors is $\frac{3 \sqrt{x}}{\sqrt{x}+1}$, that are capable of raising $300 \mathrm{~kg}$ water in 5 minutes and $50 \mathrm{~kg}$ water in 2 minutes respectively from a well of $100 \mathrm{~m}$ deep. T
A body of mass m starts moving from rest along x-axis so that its velocity varies as $\upsilon = a\sqrt s$ where a is a constant and s is the distance covered by the body. The total work done by all the forces acting on the body i
A time dependent force F = 6t acts on a particle of mass 1 kg. If the particle starts from rest, the work done by the force during the first 1 sec. will be:
A ball is dropped from a height of $20 \mathrm{~m}$. If the coefficient of restitution for the collision between ball and floor is $0.5$, after hitting the floor, the ball rebounds to a height of ________ $\mathrm{m}$.
A body is moving unidirectionally under the influence of a constant power source. Its displacement in time t is proportional to :
A uniform cable of mass 'M' and length 'L' is placed on a horizontal surface such that its (1/$n)^{th}$ part is hanging below the edge of the surface. To lift the hanging part of the cable upto the surface, the work done should be
Two particles of the same mass m are moving in circular orbits because of force, given by $F\left( r \right) = {{ - 16} \over r} - {r^3}$ The first particle is at a distance r = 1, and the second, at r = 4. The best estimate for t
A particle of mass $m$ moving in the $x$ direction with speed $2v$ is hit by another particle of mass $2m$ moving in the $y$ direction with speed $v.$ If the collision is perfectly inelastic, the percentage loss in the energy duri
A body of mass $2 \mathrm{~kg}$ begins to move under the action of a time dependent force given by $\vec{F}=\left(6 t \hat{i}+6 t^2 \hat{j}\right) N$. The power developed by the force at the time $t$ is given by:
A person pushes a box on a rough horizontal plateform surface. He applies a force of 200 N over a distance of 15 m. Thereafter, he gets progressively tired and his applied force reduces linearly with distance to 100 N. The total d
A particle is moving in a circular path of radius $a$ under the action of an attractive potential $U = - {k \over {2{r^2}}}$ Its total energy is:
A neutron moving with a speed ‘v’ makes a head on collision with a stationary hydrogen atom in ground state. The minimum kinetic energy of the neutron for which inelastic collision will take place is :
An object of mass 1000 g experiences a time dependent force $\vec{F}=\left(2 t \hat{i}+3 t^2 \hat{j}\right) N$. The power generated by the force at time $t$ is:
A particle experiences a variable force $\overrightarrow F = \left( {4x\widehat i + 3{y^2}\widehat j} \right)$ in a horizontal x-y plane. Assume distance in meters and force is newton. If the particle moves from point (1, 2) to po
A particle which is experiencing a force, given by $\overrightarrow F = 3\widehat i - 12\widehat j,$ undergoes a displacement of $\overrightarrow d = 4\overrightarrow i$ particle had a kinetic energy of 3 J at the beginning of the
A proton of mass m collides elastically with a particle of unknown mass at rest. After the collision, the proton and the unknown particle are seen moving at an angle of $90^{o}$ with respect to each other. The mass of unknown part
A body of mass 4 kg is placed on a plane at a point $P$ having coordinate $(3,4) \mathrm{m}$. Under the action of force $\overrightarrow{\mathrm{F}}=(2 \hat{i}+3 \hat{j}) \mathrm{N}$, it moves to a new point Q having coordinates $
A bullet of mass $0.1 \mathrm{~kg}$ moving horizontally with speed $400 \mathrm{~ms}^{-1}$ hits a wooden block of mass $3.9 \mathrm{~kg}$ kept on a horizontal rough surface. The bullet gets embedded into the block and moves $20 \m
In a collinear collision, a particle with an initial speed $v_{0}$ strikes a stationary particle of the same mass. If the final total kinetic energy is 50% greater than the original kinetic energy, the magnitude of the relative ve
A particle of mass $m$ moves on a straight line with its velocity increasing with distance according to the equation $v=\alpha \sqrt{x}$, where $\alpha$ is a constant. The total work done by all the forces applied on the particle
A block of mass $100 \mathrm{~kg}$ slides over a distance of $10 \mathrm{~m}$ on a horizontal surface. If the co-efficient of friction between the surfaces is 0.4, then the work done against friction $(\operatorname{in} J$) is :