Physics questions appearing in AIPMT question papers are generally simple. Here are two questions on gravitation which appeared in AIPMT 2010 question paper:

**(1)** A particle of mass *M* is situated at the centre of a spherical shell of the same mass and radius *a*. The gravitational potential at a point situated at *a*/2** **distance from the centre** **will be

(1) – 4*GM/a*

(2) – 3*GM/a*

(3) – 2*GM/a*

(4) – *GM/a*

The gravitational potential *V* at a point situated at distance* a*/2** **from the centre of the shell is equal to the sum of the gravitational potentials due to the particle of mass *M* and the shell of mass *M*.

Therefore, *V* = (– *GM*/*a*) + [– *GM*/(*a/*2)] = – 3*GM*/*a*

[Note that the gravitational potential is a *negative* quantity and that the potential due to the spherical shell is constant everywhere inside the shell and is equal to the surface value – *GM*/*a*].

(2) The radii of circular orbits of two satellites *A *and *B *of the earth are 4*R *and *R*, respectively. If the speed of satellite *A *is 3 *V*, then the speed of satellite *B *will be

(1) 3*V/*2

(2) 3*V/*4

(3) 6*V*

(4) 12*V*

The orbital speed *v *of a satellite is inversely proportional to the square root of the orbital radius *r *[since *v =*√(*Gm/r*)]. Therefore we have

*v*_{A}/*v*_{B} = √(*r*_{B}/*r*_{A})

Here *v*_{A} = 3 *V*, *r*_{A} = 4 *R* and *r*_{B} = *R* (as given in the question).

Therefore 3 *V*/*v*_{B} = √(*R/*4*R*) = ½ so that *v*_{B} *= *6 *V*

You will find some useful questions (with solution) on gravitation here as well as here.