First slide

Gravitaional potential energy

Question

The gravitational potential energy of a body of mass m at the earth's surface is -mg R_e.Its gravitational potential energy at a height R_efrom the earth's surface will be (R =radius of the earth)

Moderate

A

$- \frac{1}{2} {mgR}_{e}$
B

-2mg R_e,
C

$\frac{1}{2} {mgR}_{e}$
D

2 mg R_e

Solution

The gravitational potential ener8y at a height h above the earth's surface is given m
$U_{ph} = - \frac{{GM}_{e} m}{R_{e} + h}$
where R_e = radius of the earth.
Given h = R_e, hence
$\begin{array}{l} U_{ph} = - \frac{{GM}_{e} m}{2 R_{e}} = \frac{1}{2} [- \frac{{GM}_{e} m}{R_{e}}] \\ = \frac{1}{2} [U_{p}] = \frac{1}{2} \times (- {mgR}_{e}) \\ = - \frac{1}{2} {mgR}_{e} \end{array}$

Get Instant Solutions

When in doubt download our app. Now available Google Play Store- Doubts App

Recieve an sms with download link

Doubts App

OR

SCAN ME

Doubts App

Doubts App