Question

A particle of mass M is situated at the centre of a spherical shell of same mass and radius R. The gravitational potential at a point situated at $\frac{R}{2}$ distance from the centre will be

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

Answer 1

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

Gravitational potential at a point due to the particle at the center is
$V_1=\frac{-GM}{\frac{R}{2}}=-2\frac{GM}{R}$
The potential at the point due to the shell is $V_2=-\frac{GM}{R}$
Net potential is $V_1+V_2=\frac{-2GM}{R}+(-\frac{GM}{R})$
$=-\frac{3GM}{R}$.