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MHT CET 2024 (10 May, Shift 1) · Satellites - Orbital Velocity & Period

Satellites - Orbital Velocity & Period question from MHT CET 2024 (10 May, Shift 1)

Q22MHT CET 2024 · 10 MAY · SHIFT 1Medium

Satellites - Orbital Velocity & Period

A small planet is revolving around a very massive star in a circular orbit of radius ' $R$ ' with a period of revolution ' $T$ '. If the gravitational force between the planet and the star were proportional to ' $R^{-5/2}$ ', then ' $T$ ' would be proportional to

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Answer: (d)

Force gives the centripetal force: $m\omega^2 R \propto R^{-5/2}$ .
$\omega^2 \propto R^{-7/2}$ , and $T \propto \frac{1}{\omega}$ , so $T^2 \propto R^{7/2}$ .
$T \propto R^{7/4}$
So the answer is (d).

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