First slide

Gravitational force and laws

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 planet and star is proportional to $R^{- \frac{5}{2}}$ , then $T^{2}$ is proportional to

Moderate

A

$R^{3}$
B

$R^{7 / 2}$
C

$R^{5 / 2}$
D

$R^{3 / 2}$

Solution

For revolution of planet centripetal force is provided by gravitational force of attraction
${mω}^{2} R \propto R^{- 5 / 2} \Rightarrow \frac{1}{T^{2}} \propto R^{- 7 / 2} \Rightarrow T^{2} \propto R^{7 / 2}$

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