Question

A shell of mass $M$ and radius $R$ has a point mass $m$ placed at a distance $r$ from its centre. The gravitational potential energy $U\left(r\right)$ vs $r$ will be

• A.
• B.
• C.
• D.

Answer 1

The correct option is C

The gravitational potential energy $U\left(r\right)$ due to a shell at a distance $r$, where a point mass $m$ is placed is:
For $r\le R$:
$U\left(r\right)=-\frac{GMm}{R}$
It will be constant in negative value

For $r>R$:
$U\left(r\right)=-\frac{GMm}{r}$
It will be increasing from negative to a positive value in hyperbolic manner.

Hence, option 'c' is correct.