Question

The gravitational potential $\left(V_G\right)$ and gravitational field $\left(E_g\right)$ are plotted against distance $r$ from the centre of a uniform spherical shell. Consider the following statement
$\left(A\right)$ The plot of $V_G$ against $r$ is discontinuous.
$\left(B\right)$ The plot of $E_G$ against $r$ is discontinuous.

• A. both A and B are correct.
• B. both A and B are wrong.
• C. A is correct but B is wrong.
• D. B is correct but A is wrong.

Answer 1

The correct option is D B is correct but A is wrong.

Gravitational force on any object inside a uniform spherical shell is zero, so is the gravitational field. Thus it has exact zero value upto the radius of the shell and then suddenly varies as $-\frac{GM}{r^2}$. Hence it is discontinuous.

However the potential inside shell is constant having value equal to $-\frac{GM}{R}$ and then varies as $-\frac{GM}{r}$ outside the shell and thus is continuous at the shell boundary.