If the gravitational potential on the surface of earth is V0, then potential at a point at height half of the radius of earth is

Question

If the gravitational potential on the surface of earth is V0, then potential at a point at height half of the radius of earth is (A) (V0/2) (B) (2/3) V0 (C) (v0/3) (D) (3 V0/2)

Tardigrade Admin · Accepted Answer

Gravitational potential on the surface, V0=-(G Me/Re) Gravitational potential at height h, Vn =-(G Me/(Re+(Re)2)) =-(2/3) (G Me/Re) =(2/3) V0

Q. If the gravitational potential on the surface of earth is $V_{0}$ , then potential at a point at height half of the radius of earth is

$\frac{V _{0}}{2}$

$\frac{2}{3} V_{0}$

$\frac{v _{0}}{3}$

$\frac{3 V _{0}}{2}$

Gravitational potential on the surface,
$V_{0} = - \frac{G M _{e}}{R _{e}}$
Gravitational potential at height $h$ ,
$V_{n} = - \frac{G M _{e}}{( R _{e} + \frac{R _{e}}{2} )}$
$= - \frac{2}{3} \frac{G M _{e}}{R _{e}}$
$= \frac{2}{3} V_{0}$

Q. If the gravitational potential on the surface of earth is V0​, then potential at a point at height half of the radius of earth is

2V0​​

32​V0​

3v0​​

23V0​​