First slide

Universal law of gravitation

Question

Imagine a light planet is revolving round a very massive star in a circular orbit of radius R with a time period of revolution T. If the gravitational force of attraction between the star and planetis proportional to R^-n, then T² is proportional to

Easy

A

Rⁿ⁺¹
B

Rⁿ⁺²
C

R^n-1
D

R^n-2

Solution

$\large F\propto R^{-n}\Rightarrow F=KR^{-n}$
Gravitational Force provides necessary centripetal Force
$\large mR{\omega ^2} = K{R^{ - n}} \Rightarrow mR\frac{{4{\pi ^2}}}{{{T^2}}} = K{R^{ - n}}$
$\large {T^2} = \frac{{mR4{\pi ^2}}}{{K{R^{ - n}}}} \Rightarrow {T^2} \propto {R^{n + 1}}$

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