Consider a thin uniform spherical layer of mass M and radius R. The potential energy of gravitational interaction of matter forming this shell is
Answer & explanation
Correct answer: option 2
Let us consider the shell when a mass m is already piled on it by the agency.
If V is the potential on the shell, then
$V=-\frac{Gm}{R}$
To add a mass dm further we have
dW = Vdm
$\Rightarrow dW=-\frac{Gm}{R} dm $
$\Rightarrow W=-\frac{G}{R} \int\limits_0^{M} mdm$
$\Rightarrow W=-\frac{1}{2} \frac{GM^2}{R}$
= Potential Energy of Interaction.