Question

A particle of mass $M$ is placed at the centre of a spherical shell of equal mass and radius $a$. Then, the gravitational potential at a point $\text{P}$ at a distance $\frac{a}{2}$ from the centre is:

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

Answer 1

The correct option is B $\frac{-3Gm}{a}$


The gravitational potential at the point $\text{P}$, due to the particle at the centre is:

$V_1=-\frac{Gm}{a/2}=\frac{-2Gm}{a}$

The potential at $\text{P}$, due to the shell is:

$V_2=-\frac{GM}{a}$
Thus, net potential at $\text{p}$ is,

$V_{net}=V_1+V_2=\frac{-3Gm}{a}$

Hence, option $\left(B\right)$ is the correct answer.