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From a uniform solid sphere of mass M and radius R, a spherical cavity of radius R/2 is scooped out so that the cavity surface passes through the centre of the original sphere (its diameter lies along a radius). With V = 0 at infinity, find the gravitational potential at the centre of the cavity (G is the gravitational constant).

1. -2*G*M/(3R)
2. -2*G*M/R
3. -G*M/(2R)
4. -G*M/R

Correct answer: -G*M/R

Solution

The cavity centre is at r = R/2 from the main centre. Add the potential of the complete sphere at that point and subtract the potential of the scooped-out small sphere (evaluated at its own centre).

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