question_answer

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

A)  Zero                     

B)  \[\frac{GM}{r}\]

C)  \[-\frac{2GM}{r}\]                         

D)  \[\frac{-4\,GM}{r}\]

Correct Answer: D

Solution :

                 Gravitation potential at 0 due to the mass M at \[A,\,\,\,{{V}_{A}}\frac{-GM}{r/2}\]                 Similarly, for the mass M at B, gravitation potential \[{{V}_{B}}=-\frac{GM}{r/2}\] Total potential \[{{V}_{A}}+{{V}_{B}}=-\frac{GM}{r/2}-\frac{GM}{r/2}\]                                                 \[=-\frac{4GM}{r}\]