Question

A particle of mass M is situated at the centre of spherical shell of same mass and radius a. The gravitational potential at a point situated at a/2 distance from the centre will be

• A. $-\frac{3GM}{a}$
• B. $-\frac{2GM}{a}$
• C. $-\frac{GM}{a}$
• D. $-\frac{4GM}{a}$

Answer 1

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

Let point $A$ is situated at $a/2$ distance from the center.

Gravitational Potential at point $A$ due to spherical shell, $V_1=-\frac{GM}{a}$,

Gravitational Potential at point $A$ due to mass $M$ at point $O$ , $V_2=-\frac{GM}{\left(a/2\right)}=-\frac{2GM}{a}$,

$\therefore$ Total Gravitational Potential $=V_1+V_2=-\frac{GM}{a}-\frac{2GM}{a}=-\frac{3GM}{a}$