Suppose the gravitational force varies inversely as the n^th power of distance. Then the time period of a planet in circular orbit of radius R around - Physics MCQ AIEEE 2004 2026 | ExamTest.live | ExamTest.live

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Suppose the gravitational force varies inversely as the n^{t h} power of distance. Then the time period of a planet in circular orbit of radius R around the sun will be proportional to:

A $R^{(n + 1) /2}$
B $R^{(n - 1) /2}$
C $R^{n}$
D $R^{(n - 2) /2}$

Solution & Step-by-step Explanation

The centripetal force is provided by the modified gravitational force: \frac{m v ^{2}}{R} = \frac{k}{R ^{n}} ⟹ v^{2} \propto \frac{1}{R ^{n - 1}} ⟹ v \propto R^{(1 - n) /2} Time period T = \frac{2 π R}{v} . T \propto \frac{R}{R ^{(1 - n) /2}} = R^{1 - (1 - n) /2} = R^{(2 - 1 + n) /2} = R^{(n + 1) /2}

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Suppose the gravitational force varies inversely as the n^{t h} power of distance. Then the time period of a planet in circular orbit of radius R around the sun will be proportional to:

A

R^{(n + 1) /2}

B

R^{(n - 1) /2}

C

R^{n}

D

R^{(n - 2) /2}

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