If we did all things we are capable of, we would literally astound ourselves.

– Thomas A. Edison

Thursday, August 26, 2010

AIPMT Questions (MCQ) on Gravitation

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.