Question

Two small and heavy sphere,each of mass M,are placed a distance r apart on a horizontal surface.The gravitational potential at the midpoint on the line joining the centre of the spheres is:

• A. $0$
• B. $-\frac{GM}{r}$
• C. $-\frac{2GM}{r}$
• D. $-\frac{4GM}{r}$

Answer 1

The correct option is D $-\frac{4GM}{r}$

Gravitational potential at o due to A $=\frac{-GM}{r/2}=\frac{-2GM}{r}$

Gravitational potential at o due to B $=\frac{-GM}{r/2}=\frac{-2GM}{r}$

Total potential at 0 $=\frac{-2GM}{r}+\frac{-2GM}{r}=\frac{-4GM}{r}$