Gravitation

JEE Main level, single correct, medium

205 of 223

Question 205 of 223

A light planet is revolving around a massive star in a circular orbit of radius RR with a period of revolution T.T. If the force of attraction between planet and star is proportional to R−3/2{R}^{-3/2} then choose the correct option :

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Answer: (A) T2∝R5/2{T}^{2}\propto {R}^{5/2}

Let the gravitational force of attraction be F=GMmR3/2F=\dfrac{GMm}{{R}^{3/2}}.
Now, this gravitational force will provide the required centripetal force. Therefore,
GMmR3/2=mω2R\dfrac{GMm}{{R}^{3/2}}=m{\omega }^{2}R
⇒ω2∝1R5/2∵T=2πω\Rightarrow {\omega }^{2}\propto \dfrac{1}{{R}^{5/2}}∵T=\dfrac{2\pi }{\omega }
⇒T2∝R5/2\Rightarrow {T}^{2}\propto {R}^{5/2}

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