First slide

Gravitaional potential energy

Question

A satellite is moving in circular orbit around the earth with orbital speed v. It radius of earth is R and acceleration due to gravity on its surface is g, then height of the satellite above the surface of earth is

Moderate

A

$(\frac{2 g R^{2}}{V^{2}} - \frac{R}{2})$
B

$(\frac{g R^{2}}{V^{2}} - R)$
C

$(\frac{2 g R^{2}}{V^{2}} - R)$
D

$\frac{g R^{2}}{V^{2}}$

Solution

(2)
$\begin{array}{l} O r b i t a l s p e e d V = \sqrt{\frac{G M}{r}} \\ N o w g = \frac{G M}{R^{2}} \Rightarrow G M = g R^{2} \\ A l s o, r = R + h \\ ∴ V = \sqrt{\frac{g R^{2}}{R + h}} \Rightarrow h = (\frac{g R^{2}}{V^{2}} - R) \end{array}$

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