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) – 4GM/a
(2) – 3GM/a
(3) – 2GM/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)] = – 3GM/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 4R and R, respectively. If the speed of satellite A is 3 V, then the speed of satellite B will be
(1) 3V/2
(2) 3V/4
(3) 6V
(4) 12V
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
vA/vB = √(rB/rA)
Here vA = 3 V, rA = 4 R and rB = R (as given in the question).
Therefore 3 V/vB = √(R/4R) = ½ so that vB = 6 V
You will find some useful questions (with solution) on gravitation here as well as here.
