Q: A particle of mass m is placed at the centre of a uniform spherical shell of equal mass and radius a. Find the gravitational potential at a point P at a distance a/2 from the centre.

Sol: The gravitational potential at P due to particle at centre is

$\large V_1 = \frac{-Gm}{a/2} = – \frac{2 G m}{a}$

The potential at P due to shell is

$\large V_2 = – \frac{ G m}{a}$

The net potential at P is $\large V = V_1 + V_2 = – \frac{3 G m}{a}$