Question

A Particle of mass M is placed at the center 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 center.

Answer 1

The gravitational potential at the point $P$ due to the particle at the centre is

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

The potential at $P$ due to the shell is

$V_2=\frac{-GM}{a}$

The net potential at $P$ is

$V_1+V_2=\frac{-3GM}{a}$

$\downarrow$

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