Question

Let $V$ and $E$ denote the gravitational potential and gravitational field at a point. It is possible to have

• A. $V=0$ and $E=0$
• B. $V=0$ and $E\ne 0$
• C. $V\ne 0$ and $E=0$
• D. $V\ne 0$ and $E\ne 0$

Answer 1

Answer: (A), (B), (C), (D)

The correct options are
A $V=0$ and $E=0$
B $V=0$ and $E\ne 0$
C $V\ne 0$ and $E=0$
D $V\ne 0$ and $E\ne 0$

A) At $\infty$ both $V$ and $E$ are zero.
B) Let, $V_{\infty }=\frac{GM}{R}$ for an unit mass. So, $V_R=0$ i.e. at the radius R of solid sphere(mass M) and $E_R=\frac{GM}{R^2}$
C) Inside a spherical shell $V=\frac{-GM}{R}$ and $E=0$
D) Consider a point at a distance of $r$ from mass $m$. Then, $V=\frac{-GM}{r}$ and $E=\frac{GM}{r^2}$.