Question 1

A body which is initially at rest at a height R above the surface of the Earth of radius R, falls freely towards the Earth, then its velocity on reaching the surface of the Earth is

Accepted Answer

Increase in kinetic energy = Decrease in potential energy aligned & 1 2 m v^2= m g R 1+ R R = m g R 2 ( U= m g h 1+ h R , h=R ) \ & m v^2=m g R v= g R aligned

Question 2

The distance between Sun and Earth is R. The duration of year if the distance between Sun and Earth becomes 3 R will be:

Accepted Answer

Basically 1 year is equal to time period of earth revolution around sun. So, T_i=1 year Now, T^2 R^3 ( T_2 T_1 )^2= ( R_2 R_1 )^3 T_2= ( R_2 R_1 )^ 3 / 2 T_1= ( 3 R R )^ 3 / 2 1 =3 3 years.

Question 3

For a particle inside a uniform spherical shell, the gravitational force on the particle is

Accepted Answer

Various regions of spherical shell attract the point mass inside it in various directions. These forces cancel each other completely. Therefore the gravitational force on the particle is zero.

Question 4

The kinetic energy of a satellite in its orbit around the earth is E . What should be the kinetic energy of the satellite so as to enable it to escape from the gravitational pull of the earth?

Accepted Answer

We know that v_e= 2 v_0, where v _0 is orbital velocity. K.E. in the orbit, E= 1 2 M v_0 ^2 K.E. to escape E= 1 2 M v_e^2= 1 2 M (2 v_0 ^2 ) = 1 2 M v_0^2 2=2 E

Question 5

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:

Accepted Answer

Radius of circle, r = a Centrifugal force, F=m ^2 r aligned & Gmm (2 a )^2 = m ^2 a \ & ( F = G M M _2 ~d ) aligned Here M_1=m ; M_2=m and d=2 a angular speed, = G m 4 a^3

Question 6

If 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:

Accepted Answer

Potential due to sphere V = GM 2 R ^3 (3 R ^2- r ^2 ) At surface r=R V= ( G M R ) At centre, r=0 V _0= 3 GM 2 R = ( 3 ~V 2 )

Question 7

Two planets A and B of radii R and 1.5 R have densities and / 2 respectively. The ratio of acceleration due to gravity at the surface of B to A is :

Accepted Answer

Acceleration due to gravity, g = GM R ^2 = 4 3 G R g_2 g_1 = _2 _1 R_2 R_1 = 1 2 1.5= 3 4

Question 8

Suppose the law of gravitational attraction suddenly changes and becomes an inverse cube law i.e. F 1 r^ 3 , but still remaining a central force. Then

Accepted Answer

According to kepler's law of area d A dt = L 2 ~m For central forces, torque =0 L = constant d A dt = constant

Question 9

A point particle is held on the axis of a ring of mass m and radius r at a distance r from its centre C. When released, it reaches C under the gravitational attraction of the ring. Its speed at C will

Accepted Answer

Let ' M ' be the mass of the particle Now, E_ initial =E_ final i.e. GMm 2 r +0= GM m r + 1 2 MV ^ 2 or, 1 2 MV ^ 2 = GM m r [1- 1 2 ] 1 2 ~V ^ 2 = G m r [1- 1 2 ] or, V = 2 Gm r (1- 1 2 )

Gravitation — Previous Year Questions & Solutions