Question

Two concentric shells have masses $M$ and $m$ and their radii are $R$ and $r$, respectively, where $R>r$. What is the gravitational potential at their common centre?

• A. $-\frac{GM}{R}$
• B. $-\frac{GM}{r}$
• C. $-G[\frac{M}{R}-\frac{m}{r}]$
• D. $-G[\frac{M}{R}+\frac{m}{r}]$

Answer 1

Answer: (D)

$-G[\frac{M}{R}+\frac{m}{r}]$

$\text{Gravitational potential at the centre of a spherical shell}=\text{Gravitational Potential on surface}$

$=-G\times \frac{\text{mass of shell}}{\text{radius}}$

$\therefore$ gravitational potential at their common center $=-G[\frac{M}{R}+\frac{m}{r}]$