First slide

Keplers 3 Laws

Question

U the gravitational force is proportional to 1/ R³ , the square of time period of revolution is proportional to

Moderate

A

R²
B

R³
C

R⁴
D

None

Solution

$F = k / R^{3}$
Now $\frac{{mv}^{2}}{R} = \frac{k}{R^{3}} or V = \frac{1}{R} \sqrt{(\frac{k}{m})}$
The frequency of revolution v is given by
$v = \frac{V}{2 πR}$
So, the time period of revolution
$T = \frac{1}{v} = \frac{2 πR}{V} = 2 {πR}^{2} \sqrt{(\frac{m}{k})}$
or $T \propto R^{2} or T^{2} \propto R^{4}$

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