Question

Let $V_G$ and $E_G$ denote gravitational potential and field respectively, the it is possible to have

• A. $V_G=0,E_G=0$
• B. $V_G\ne 0,E_g=0$
• C. $V_G=0,E_g\ne 0$
• D. $V_G\ne 0,E_G\ne 0$

Answer 1

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

The correct options are
A $V_G=0,E_G=0$
B $V_G\ne 0,E_g=0$
C $V_G=0,E_g\ne 0$
D $V_G\ne 0,E_G\ne 0$

A) At $\infty$ both $V$ and $E$ are zero.

B) Let, $V_{\infty }=\frac{GM}{R}\to V_R=0$ 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 $E=\frac{GM}{r^2}$.