Question

P is a point at a distance r from the centre of a spherical shell of mass M and radius a, where $r<a$. The gravitational potential at P is?

• A. $-3\frac{GM}{r}$
• B. $-\frac{GM}{a}$
• C. $-GM\frac{r}{a^2}$
• D. $-GM\left(\frac{a-r}{a^2}\right)$

Answer 1

The correct option is A $-3\frac{GM}{r}$

Potential at the surface of the shell = Potential due to particle + Potential due to shell

=$\frac{GM}{R}+2\frac{-GM}{R}$

$=-3\frac{GM}{R}$