Question

Which of the following curve represents the variation of gravitational potential of a hollow sphere of radius $R$ with radial distance $\left(r\right)$?

• A.
• B.
• C.
• D.

Answer 1

The correct option is C

Let the mass of the hollow sphere is $M$ and radius is $R$.

Let us assume that the distance from the centre of sphere to a random point is $r$

Case I: When $r\le R$

The gravitational potential is given by
$V_{in}=\frac{-GM}{R}$
So, gravitational potential inside the hollow sphere is constant.

Case II: When $r>R$

The gravitational potential is given by

$V_{out}=\frac{-GM}{r}$
So, $V_{out}\propto \frac{-1}{r}$

The potential remains constant inside the sphere and it is equal to potential at the surface and increase when the point moves away from the surface of the sphere.

Hence, the correct option is (c).

Why this question? To make students familiar with the graphs of variation of gravitational potential in case of hollow sphere. This is a frequently asked category of question.