First slide

Motion of planets and satellites

Question

Imagine a light planet revolving around a very massive star in a circular orbit of radius R with a period of revolution T. If the gravitational force of attraction between the planet and the star is proportional to $R^{+ 5 / 2}$ , then

Moderate

A

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

$T^{2} \propto R^{7 / 2}$
C

$T^{2} \propto R^{3 / 2}$
D

$T^{2} \propto R^{3 / 76}$

Solution

The gravitational force $F \propto \frac{1}{R^{\frac{5}{2}}} (given)$
$F = \frac{C}{R^{\frac{5}{2}}} - - - - - (1)$ here C is constant
The centripetal force for the planet $= m R ω^{2} = m R {(\frac{2 π}{T})}^{2} - - - - - (2)$
Centripetal force is provided from gravitational force (1) = (2)
$F = \frac{C}{R^{\frac{5}{2}}} = m R {(\frac{2 π}{T})}^{2}$
$\Rightarrow T^{2} \propto R^{\frac{5}{2}} R$
$\Rightarrow T^{2} \propto R^{\frac{7}{2}}$
Therefore, the correct answer is (B)

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