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Question

Physics Question on Gravitational Potential Energy

Two spheres each of mass MM and radius RR are separated by a distance of rr. The gravitational potential at the midpoint of the line joining the centres of the spheres is

A

−GMr - \frac{GM}{r}

B

−2GMr - \frac{2GM}{r}

C

−GM2r - \frac{GM}{2r}

D

−4GMr - \frac{4GM}{r}

Answer

−4GMr - \frac{4GM}{r}

Explanation

Solution

Let PP be the midpoint of the line joining the centres of the spheres, The gravitational potential at point PP is Vp=GMr/2−GMr/2V_{p} = \frac{GM}{r/2} - \frac{GM}{r/2} =−2GMr−2GMr=−4GMr= - \frac{2GM}{r} - \frac{2GM}{r}=- \frac{4GM}{r}