First slide

Gravitational force and laws

Question

If $g \propto \frac{1}{R^{3}}$ (instead of $\frac{1}{R^{2}}),$ then the relation between time period of a satellite near earth's surface and radius R will be

Easy

A

$T^{2} \propto R^{3}$
B

$T \propto R^{2}$
C

$T^{2} \propto R$
D

$T \propto R$

Solution

Gravitational force provides the required centripetal force $m ω^{2} R = \frac{G M m}{R^{3}} \Rightarrow \frac{4 π^{2}}{T^{2}} = \frac{G M}{R^{4}} \Rightarrow T^{2} \propto R^{4} \Rightarrow T \propto R^{2}$

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