Question

Four 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. $-\frac{4GM}{r}$

Answer 1

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

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

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

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