# Suppose the gravitational force varies inversely as the  nth power of distance. Then the time period of a planet in circular orbit of radius  R  around the sun will be proportional to : Option 1) Option 2) Option 3) Option 4)

As we learnt in

For motion of a planet in circular orbit,

Centripetal force = Gravitational force

$\dpi{100} \therefore \; \; mR\omega ^{2}=\frac{GMm}{R^{n}}\; \; or\; \; \omega =\sqrt{\frac{GM}{R^{n+1}}}$

$\dpi{100} \therefore \; \; \; T=\frac{2\pi }{\omega }=2\pi \sqrt{\frac{R^{n+1}}{GM}}=\frac{2\pi }{\sqrt{GM}}R^{\left ( \frac{n+1}{2} \right )}$

$\dpi{100} \therefore \; \; T\; is\; proportional\; to\; R^{\left ( \frac{n+1}{2} \right )}$

Newton's Law of Gravitation -

Force

Gravitalional constant

Masses

Distance between masses

- wherein

Force is along the line joining the two masses

Option 1)

Correct

Option 2)

Incorrect

Option 3)

Incorrect

Option 4)

Incorrect

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