##
Two spherical planets P and Q have the same uniform density , masses MP and MQ, and surface areas A and 4A, respectively. A spherical planet R also has uniform density and its mass is (MP + MQ). The escape velocities from the planets P, Q and R, are VP, VQ and VR, respectively. ThenTwo spherical planets P and Q have the same uniform density, masses MP and MQ, and surface areas A and 4A, respectively. A spherical planet R also has uniform density and its mass is (MP + MQ). The escape velocities from the planets P, Q and R, are VP, VQ and VR, respectively. Then

Two spherical planets P and Q have the same uniform density , masses MP and MQ, and surface areas A and 4A, respectively. A spherical planet R also has uniform density and its mass is (MP + MQ). The escape velocities from the planets P, Q and R, are VP, VQ and VR, respectively. ThenTwo spherical planets P and Q have the same uniform density, masses MP and MQ, and surface areas A and 4A, respectively. A spherical planet R also has uniform density and its mass is (MP + MQ). The escape velocities from the planets P, Q and R, are VP, VQ and VR, respectively. Then

##
Two bodies, each of mass M, are kept fixed with a separation 2L. A particle of mass m is projected from the midpoint of the line joining their centres, perpendicular to the line. The gravitational constant is G. The correct statement(s) is (are)

Two bodies, each of mass M, are kept fixed with a separation 2L. A particle of mass m is projected from the midpoint of the line joining their centres, perpendicular to the line. The gravitational constant is G. The correct statement(s) is (are)

##
Suppose the radius of earth is half of its present value (Mass remaining unchanged). The value of g at a height equal to the final radius is 10x m/s2. Find the value of x.

Suppose the radius of earth is half of its present value (Mass remaining unchanged). The value of g at a height equal to the final radius is 10x m/s2. Find the value of x.

##
A point mass when enters d depth below the earth’s surface such that the g reduces by 1% then the value of d is [Take Re = 6400 km]

A point mass when enters d depth below the earth’s surface such that the g reduces by 1% then the value of d is [Take Re = 6400 km]

##
The ratio between masses of two planets is 3 : 5 and the ratio between their radii is 5 : 3. The ratio between

their acceleration due to gravity will be

their acceleration due to gravity will be

The ratio between masses of two planets is 3 : 5 and the ratio between their radii is 5 : 3. The ratio between

their acceleration due to gravity will be

##
The weight of an object on the surface of the Earth is 40 N. Its weight at a height equal to the radius of the Earth is

The weight of an object on the surface of the Earth is 40 N. Its weight at a height equal to the radius of the Earth is

##
Two spherical planets P and Q have the same uniform density , masses MP and MQ, and surface areas A and 4A, respectively. A spherical planet R also has uniform density and its mass is (MP + MQ). The escape velocities from the planets P, Q and R, are VP, VQ and VR, respectively. ThenTwo spherical planets P and Q have the same uniform density, masses MP and MQ, and surface areas A and 4A, respectively. A spherical planet R also has uniform density and its mass is (MP + MQ). The escape velocities from the planets P, Q and R, are VP, VQ and VR, respectively. Then

##
Two bodies, each of mass M, are kept fixed with a separation 2L. A particle of mass m is projected from the midpoint of the line joining their centres, perpendicular to the line. The gravitational constant is G. The correct statement(s) is (are)

##
Suppose the radius of earth is half of its present value (Mass remaining unchanged). The value of g at a height equal to the final radius is 10x m/s2. Find the value of x.

##
Which of the following quantities related to planets remains same during their motion in elliptical orbits as seen from the sun?

Which of the following quantities related to planets remains same during their motion in elliptical orbits as seen from the sun?

##
The time period of a satellite of the earth is 10 hours. If the separation between the earth and the satellite is increased to 4 times the previous value, then what will be the new time period of the satellite?

The time period of a satellite of the earth is 10 hours. If the separation between the earth and the satellite is increased to 4 times the previous value, then what will be the new time period of the satellite?

##
A planet is at R distance from sun and its time period of revolution is T. What will be its new time period of revolution if it is brought 0.5 R distance closer to sun?

A planet is at R distance from sun and its time period of revolution is T. What will be its new time period of revolution if it is brought 0.5 R distance closer to sun?

##
If the change in value of g at a height h above the surface of the earth is same as that at a depth d below it, when both h and d are much smaller than the radius of the earth, then

If the change in value of g at a height h above the surface of the earth is same as that at a depth d below it, when both h and d are much smaller than the radius of the earth, then

##
If the radius of earth were to shrink by one percent and mass remains same, then acceleration due to gravity on the surface of the earth would

If the radius of earth were to shrink by one percent and mass remains same, then acceleration due to gravity on the surface of the earth would

## A stone is dropped from a minar of height h and it reaches after t seconds on earth. From the same minar if two stones are thrown (one upwards and other downwards) with the same velocity u and they reach the earth surface after t1 and t2 seconds respectively, then

A stone is dropped from a minar of height h and it reaches after t seconds on earth. From the same minar if two stones are thrown (one upwards and other downwards) with the same velocity u and they reach the earth surface after t1 and t2 seconds respectively, then

## A ball is projected upwards from a height h above the surface of the earth with velocity v. The time at which the ball strikes the ground is

A ball is projected upwards from a height h above the surface of the earth with velocity v. The time at which the ball strikes the ground is

## A man throws balls with the same speed vertically upwards, one after the other at an interval of 2 seconds. What should be the speed of the throw so that more than two balls are in the sky at any time? (Given g = 9.8 m/s2)

A man throws balls with the same speed vertically upwards, one after the other at an interval of 2 seconds. What should be the speed of the throw so that more than two balls are in the sky at any time? (Given g = 9.8 m/s2)

## A car is moving with c/2 a stone is thrown from the car with speed c/root 2 at 45 degree with the direction of velocity of the car. What is the angle as seen from the ground?

A car is moving with c/2 a stone is thrown from the car with speed c/root 2 at 45 degree with the direction of velocity of the car. What is the angle as seen from the ground?

## A car starts moving rectilinearly, first with acceleration 5 m/s^2 (the initial velocity is equal to zero), then uniformly , and finaly , decelerating at the same rate, comes to stop.Total time of motion equals to 25 sec . The avg velocity during that time is equal to 72 km/hr .How long does the car move uniformly?

A car starts moving rectilinearly, first with acceleration 5 m/s^2 (the initial velocity is equal to zero), then uniformly , and finaly , decelerating at the same rate, comes to stop.Total time of motion equals to 25 sec . The avg velocity during that time is equal to 72 km/hr .How long does the car move uniformly?

## Find the angle of projection at when horizontal range and maximum height of a projectile are equal?

Find the angle of projection at when horizontal range and maximum height of a projectile are equal?

## A swimmer wants to reach to a point just opposite on the other bank of the river. How should he swim and why?

A swimmer wants to reach to a point just opposite on the other bank of the river. How should he swim and why?

## A ball is dropped gently from the top of tower and another ball is thrown horizontally at same time.Which ball will hit the ground first?

A ball is dropped gently from the top of tower and another ball is thrown horizontally at same time.Which ball will hit the ground first?

## A stone is projected horizontally with 20 m/s from top of a tall building. Calculate its position and velocity after 3 sec neglecting the air resistance?

A stone is projected horizontally with 20 m/s from top of a tall building. Calculate its position and velocity after 3 sec neglecting the air resistance?

## A stone is projected horizontally with 20 m/s from top of a tall building. Calculate its position and velocity after 3 sec neglecting the air resistance?

## If the displacement of a body is proportional of square of time, state whether the body is moving with uniform velocity or uniform acceleration?

If the displacement of a body is proportional of square of time, state whether the body is moving with uniform velocity or uniform acceleration?

## Two stones P and Q of different masses m and 2m respectively are dropped simultaneously from top of a tower and reach the ground with different energies . Which one is faster?

Two stones P and Q of different masses m and 2m respectively are dropped simultaneously from top of a tower and reach the ground with different energies . Which one is faster?

## Can an object with constant acceleration reverse its direction of travel ? Explain

Can an object with constant acceleration reverse its direction of travel ? Explain

##
If L, C and R represent inductance, capacitance and resistance respectively, then which of the following does not represent dimensions of frequency?

If L, C and R represent inductance, capacitance and resistance respectively, then which of the following does not represent dimensions of frequency?

##
Number of particles crossing unit area perpendicular to X-axis in unit time is given by

n =

are number of particles per unit volume in the position x1 and x2. Find dimensions of D called as diffusion constant

Number of particles crossing unit area perpendicular to X-axis in unit time is given by

n =

are number of particles per unit volume in the position x1 and x2. Find dimensions of D called as diffusion constant

##
X = 3YZ*Z find dimensions of Y in (MKSA) system, if X and Z are the dimensions of capacity and magnetic field respectively

X = 3YZ*Z find dimensions of Y in (MKSA) system, if X and Z are the dimensions of capacity and magnetic field respectively

##
Wavelength of ray of light is 0.00006 m. It is equal to

Wavelength of ray of light is 0.00006 m. It is equal to

##
What is the relationship between dyne and newton of force?

What is the relationship between dyne and newton of force?

##
The magnitude of any physical quantity

The magnitude of any physical quantity

##
If the constant of gravitation (G), Planck's constant (h) and the velocity of light (c) be chosen as fundamental units. The dimensions of the radius of gyration is

If the constant of gravitation (G), Planck's constant (h) and the velocity of light (c) be chosen as fundamental units. The dimensions of the radius of gyration is

## A projectile is launched with an initial velocity of 30 m/s at angle of 60 degree above the horizontal. Calculate the magnitude and direction of its velocity 5s after launch?

A projectile is launched with an initial velocity of 30 m/s at angle of 60 degree above the horizontal. Calculate the magnitude and direction of its velocity 5s after launch?

## An object is dropped from the top of the tower of height 156.8 m and the same time another object is thrown vertically upward with velocity of 78.1 mm/s from the foot of the tower, find when and where two object meet?

An object is dropped from the top of the tower of height 156.8 m and the same time another object is thrown vertically upward with velocity of 78.1 mm/s from the foot of the tower, find when and where two object meet?

##
A cannon fires successively two shells from the same point with velocity v0 = 250m/s ; the first at the angle =60° and the second at the angle =45° to the horizontal, the azimuth being the same. Neglecting the air drag, find the approximate time interval between firings leading to the collision of the shells (g = 9.8 m/s2.)

A cannon fires successively two shells from the same point with velocity v0 = 250m/s ; the first at the angle =60° and the second at the angle =45° to the horizontal, the azimuth being the same. Neglecting the air drag, find the approximate time interval between firings leading to the collision of the shells (g = 9.8 m/s2.)

##
Each of the two block shown in the figure has mass m. The pulley is smooth and the coefficient of friction for all surfaces in contact is . A constant horizontal force P applied in two cases shown in such a way that block A start just sliding then the value of minimum force P in case-I and case-II is :

Each of the two block shown in the figure has mass m. The pulley is smooth and the coefficient of friction for all surfaces in contact is . A constant horizontal force P applied in two cases shown in such a way that block A start just sliding then the value of minimum force P in case-I and case-II is :

##
A particle is projected with speed 30m/s at angle 22.5° with horizontal from ground as shown. AB and CD are parallel to y-axis and B is highest point of trajectory of particle. CD/AB is

A particle is projected with speed 30m/s at angle 22.5° with horizontal from ground as shown. AB and CD are parallel to y-axis and B is highest point of trajectory of particle. CD/AB is

##
A block of mass m is pulled on an incline surface having coefficient of friction = 1 & angle of inclination = 30°, with the horizontal, such that required external force is minimum. The angle made by this force with the incline is :

A block of mass m is pulled on an incline surface having coefficient of friction = 1 & angle of inclination = 30°, with the horizontal, such that required external force is minimum. The angle made by this force with the incline is :

##
A body falls freely from the top of a tower and during the last second of its fall it falls through 25 m. Find the height of tower?

A body falls freely from the top of a tower and during the last second of its fall it falls through 25 m. Find the height of tower?

##
A ball is thrown velocity with a velocity V at an angle theta with the horizontal .Can an another angle of projection achieve the some horizontal range.Justify your answer?

A ball is thrown velocity with a velocity V at an angle theta with the horizontal .Can an another angle of projection achieve the some horizontal range.Justify your answer?

##
A ball is dropped from high rise platform at t =0 starting from rest.After 6 second another ball is thrown downwards from same platform with speed v.The two ball meets at t = 18s .find thee value of v (g = 10 m/s*s)

A ball is dropped from high rise platform at t =0 starting from rest.After 6 second another ball is thrown downwards from same platform with speed v.The two ball meets at t = 18s .find thee value of v (g = 10 m/s*s)

##
A uniform rope of length 'L' is hanging off the edge of a rough table having coefficient of static friction u.What should be minimum length of hanging part so that the rope starts sliding down?

A uniform rope of length 'L' is hanging off the edge of a rough table having coefficient of static friction u.What should be minimum length of hanging part so that the rope starts sliding down?

##
Two particles of masses m1,m2 and charges q1,q2 placed r0 distance apart on a smooth horizontal surface.Due to electrostatic repulsion they move away from each other.Ratio of their kinetic energy at a later time is

Two particles of masses m1,m2 and charges q1,q2 placed r0 distance apart on a smooth horizontal surface.Due to electrostatic repulsion they move away from each other.Ratio of their kinetic energy at a later time is

##
A body is projected horizontally from the top of tower 100m high with a velocity at 9.8 m/s.Find the velocity with which hits the ground?

A body is projected horizontally from the top of tower 100m high with a velocity at 9.8 m/s.Find the velocity with which hits the ground?

##
A projectile is fired from the ground level with a velocity of 500m/s at 30 degree to horizontal range and greatest hight to which it rises.What is the least speed with which could be projected in order to achieve the same

A projectile is fired from the ground level with a velocity of 500m/s at 30 degree to horizontal range and greatest hight to which it rises.What is the least speed with which could be projected in order to achieve the same

##
A projectile is fired from the level with velocity 150 m/s at 30 degree to the horizontal.Find its horizontal range. What will be the least speed to achieve some horizontal range?

A projectile is fired from the level with velocity 150 m/s at 30 degree to the horizontal.Find its horizontal range. What will be the least speed to achieve some horizontal range?

##
From a flying aeroplane a body should be dropped in advance to hit the target why?

From a flying aeroplane a body should be dropped in advance to hit the target why?

## A hollow spherical ball is filled up with sand. Sand comes out through a hole at the bottom. Time period of oscillation?

A hollow spherical ball is filled up with sand. Sand comes out through a hole at the bottom. Time period of oscillation?

## A spring pendulum is taken from pole to equator. Its time period

A spring pendulum is taken from pole to equator. Its time period

##
Time period of a simple pendulum of length 95 and amplitude 1 cm is 4 s. If amplitude is made 2 cm, then time period is

Time period of a simple pendulum of length 95 and amplitude 1 cm is 4 s. If amplitude is made 2 cm, then time period is

##
A 0.1 kg mass is suspended from a wire of negligible mass. The length of the wire is 1 m and its cross- sectional area is 4.9 × 10–7 m2. If the mass is pulled a little in the vertically downward direction and released, it performs simple harmonic motion of angular frequency 140 rad s–1. If the Young's modulus of the material of the wire is n × 109 Nm–2, the value of n is

A 0.1 kg mass is suspended from a wire of negligible mass. The length of the wire is 1 m and its cross- sectional area is 4.9 × 10–7 m2. If the mass is pulled a little in the vertically downward direction and released, it performs simple harmonic motion of angular frequency 140 rad s–1. If the Young's modulus of the material of the wire is n × 109 Nm–2, the value of n is

##
Two simple pendulum have lengths l and 25l/16 . At t = 0 they are in same phase. After how many oscillations of smaller pendulum will they be again in phase for first time ?

Two simple pendulum have lengths l and 25l/16 . At t = 0 they are in same phase. After how many oscillations of smaller pendulum will they be again in phase for first time ?

## A particle is thrown upward vertically with initial speed root gre where g is acceleration due to gravity on earth's surface.What is the maximum height attain by the particle?

A particle is thrown upward vertically with initial speed where g is acceleration due to gravity on earth's surface.What is the maximum height attain by the particle?

## Find the free fall time of a test mass on an object of Mass M from a height 2R to R?

Find the free fall time of a test mass on an object of Mass M from a height 2R to R?

## A Constant force f is applied on a particle of mass 'm' which is initially at rest. As the particle starts moving a resistive force -bv begins to act on it.Speed of the particle at any instant of time 't' is?

A Constant force f is applied on a particle of mass 'm' which is initially at rest. As the particle starts moving a resistive force -bv begins to act on it.Speed of the particle at any instant of time 't' is?

## A particle of mass m is thrown with initial speed V0 .A resistance force -kv acts on the particle .Distance moved by particle in time t is?

## A motor boat going down stream over came a raft at a point A, t = 60 min later it turned back and after some time passed the raft at a distance l = 6.0 km from the point A. Find the flow velocity assuming the duty of the engine to be constant?

A motor boat going down stream over came a raft at a point A, t = 60 min later it turned back and after some time passed the raft at a distance l = 6.0 km from the point A. Find the flow velocity assuming the duty of the engine to be constant?

## A current carrying wire heats a metal rod. The wire provides a constant power (P) to the rod. The metal rod is enclosed in an insulated container. It is observed that the temperature (T) in the metal rod changes with time (t) as

A current carrying wire heats a metal rod. The wire provides a constant power (P) to the rod. The metal rod is enclosed in an insulated container. It is observed that the temperature (T) in the metal rod changes with time (t) as

Where is a constant with appropiate dimension with is a constant with dimension of temperature .

The heat capacity of the metal is?

## What is maximum acceleration so that so that two block move together?

What is maximum acceleration so that so that two block move together?

## Two particles of masses m1 and m2 are placed 'd' distance apart. Due to gravitational attraction they move towards each other.What is speed of m1 when their separation reduces to d/2.

Two particles of masses m1 and m2 are placed 'd' distance apart. Due to gravitational attraction they move towards each other.What is speed of m1 when their separation reduces to d/2.

## Two particle of masses m1 and m2 are 'd' distance apart. Due to gravitational attraction they move towards each other. what is speed of m1 when their separation reduces to d/2.

Two particle of masses m1 and m2 are 'd' distance apart. Due to gravitational attraction they move towards each other. what is speed of m1 when their separation reduces to d/2.

## A current I flows in an infinitely long wire with a cross-section in the form of a semicircular ring of radius R. What is the magnitude of the magnetic induction along its axis?

A current *I* flows in an infinitely long wire with a cross-section in the form of a semicircular ring of radius *R*. What is the magnitude of the magnetic induction along its axis?

## A Carnot engine operating between temperatures T1 and T2 has efficiency 1/6. When T2 is lowered by 62 K, its efficiency increases to 1/3. Then what will be T1 and T2 ?

A Carnot engine operating between temperatures *T _{1}* and

*T*has efficiency 1/6. When

_{2}*T*is lowered by 62 K, its efficiency increases to 1/3. Then what will be

_{2}*T*and

_{1}*T*

_{2 }?

## An object moving with a speed of 6.25 m s-1, is decelerated at a rate given by , where v is the instantaneous speed. What would be the time taken by the object to come to rest?

An object moving with a speed of *6.25 m s ^{-1}*, is decelerated at a rate given by , where

*v*is the instantaneous speed. What would be the time taken by the object to come to rest?

## The electrostatic potential inside a charged spherical ball is given by where r is the distance from the centre; a, b are constants. Then the charge density inside the ball is

The electrostatic potential inside a charged spherical ball is given by where *r* is the distance from the centre; *a, b* are constants. Then the charge density inside the ball is

## A car is fitted with a convex side-view mirror of focal length 20 cm. A second car 2.8 m behind the first car is overtaking the first car at a relative speed of 15 m s-1. The speed of the image of the second car as seen in the mirror of the first one is

A car is fitted with a convex side-view mirror of focal length 20 cm. A second car 2.8 m behind the first car is overtaking the first car at a relative speed of 15 m s^{-1}. The speed of the image of the second car as seen in the mirror of the first one is

## If a wire is stretched to make it 0.1% longer, its resistance will

If a wire is stretched to make it 0.1% longer, its resistance will

## Three perfect gases at absolute temperatures T1, T2 and T3 are mixed. The masses of molecules are m1, m2 and m3 and the number of molecules are n1, n2 and n3 respectively. Assuming no loss of energy, the final temperature of the mixture is

Three perfect gases at absolute temperatures *T _{1}, T_{2}* and

*T*are mixed. The masses of molecules are

_{3}*m*and

_{1}, m_{2}*m*and the number of molecules are

_{3}*n*and

_{1}, n_{2}*n*respectively. Assuming no loss of energy, the final temperature of the mixture is

_{3}## Two identical charged spheres suspended from a common point by two massless strings of length l are initially a distance d(d < < l) apart because of their mutual repulsion. The charge begins to leak from both the spheres at a constant rate. As a result the charges approach each other with a velocity v. Then as a function of distance x between them

Two identical charged spheres suspended from a common point by two massless strings of length *l* are initially a distance *d(d < < l)* apart because of their mutual repulsion. The charge begins to leak from both the spheres at a constant rate. As a result the charges approach each other with a velocity *v*. Then as a function of distance x between them

## Work done in increasing the size of a soap bubble from a radius of 3 cm to 5 cm is nearly. [Surface tension of soap solution = 0.03 N m-1]

Work done in increasing the size of a soap bubble from a radius of 3 cm to 5 cm is nearly.

[Surface tension of soap solution = 0.03 N m^{-1}]

## A fully charged capacitor C with initial charge q0 is connected to a coil of self-inductance L at t = 0. What is the time at which the energy is stored equally between the electric and the magnetic fields?

A fully charged capacitor *C* with initial charge *q _{0}* is connected to a coil of self-inductance

*L*at

*t = 0*. What is the time at which the energy is stored equally between the electric and the magnetic fields?

## Two bodies of masses m and 4m are placed at a distance r. What will be the gravitational potential at a point on the line joining them where the gravitational field is zero?

Two bodies of masses *m* and *4m* are placed at a distance *r*. What will be the gravitational potential at a point on the line joining them where the gravitational field is zero?

## A thin horizontal circular disc is rotating about a vertical axis passing through its centre. An insect is at rest at a point near the rim of the disc. The insect now moves along a diameter of the disc to reach its other end. During the journey of the insect, what will be the angular speed of the disc?

A thin horizontal circular disc is rotating about a vertical axis passing through its centre. An insect is at rest at a point near the rim of the disc. The insect now moves along a diameter of the disc to reach its other end. During the journey of the insect, what will be the angular speed of the disc?

## Let the x–z plane be the boundary between two transparent media. Medium 1 in z ≥ 0 has a refractive index of 2 and medium with z < 0 has a refractive index of . A ray of light in medium 1 given by the vector is incident on the plane of separation. What will be the angle of refraction in medium 2?

Let the *x–z* plane be the boundary between two transparent media. Medium 1 in *z ≥ 0* has a refractive index of 2 and medium with *z < 0* has a refractive index of . A ray of light in medium 1 given by the vector is incident on the plane of separation. What will be the angle of refraction in medium 2?

## Two particles are executing simple harmonic motion of the same amplitude A and frequency w along the x-axis. Their mean position is separated by distance X0 (X0 > A). If the maximum separation between them is (X0 + A), the phase difference between their motion is

Two particles are executing simple harmonic motion of the same amplitude *A* and frequency w along the *x-axis*. Their mean position is separated by distance *X _{0} (X_{0} > A)*. If the maximum separation between them is (

*X*), the phase difference between their motion is

_{0}+ A## Direction: The question has a paragraph followed by two statements, Statement-1 and Statement-2. Of the given four alternatives after the statements, choose the one that describes the statements. A thin air film is formed by putting the convex surface of a plane-convex lens over a plane glass plate. With monochromatic light, this film gives an interference pattern due to light reflected from the top (convex) surface and the bottom (glass plate) surface of the film. Statement-1: When light reflects from the air-glass plate interface, the reflected wave suffers a phase change of p. Statement-2: The centre of the interference pattern is dark.

**Direction:** The question has a paragraph followed by two statements, Statement-1 and Statement-2. Of the given four alternatives after the statements, choose the one that describes the statements.

A thin air film is formed by putting the convex surface of a plane-convex lens over a plane glass plate. With monochromatic light, this film gives an interference pattern due to light reflected from the top (convex) surface and the bottom (glass plate) surface of the film.

**Statement-1:** When light reflects from the air-glass plate interface, the reflected wave suffers a phase change of p.

**Statement-2:** The centre of the interference pattern is dark.