Question

A particle of mass M is situated at the centre of a spherial shell of same mass and radius R. The gravitational potential at a point situated at $R2$ 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 $-\frac{3GM}{R}$

Here, mass of the particle=M, Mass of the spherical shell=M, Radius of the spherical shell= R. Let O be centre of spherical shell. Gravitational potential at point P diue to particle at O is $V_1=\frac{GM}{\left(R/2\right)}$

Gravitational potential at point P due to spherical shell is $V_2=\frac{GM}{R}$

Hence, total gravitational potential at point P is $V=V_1+V_2$

$=-\frac{GM}{\left(R/2\right)}+(-\frac{GM}{R})=-\frac{2GM}{R}-\frac{GM}{R}=-\frac{3GM}{R}$