JEE Main On 08 April 2018 Question 30

Question: A particle is moving with a uniform speed in a circular orbit of radius R in a central force inversely proportional to the $ {n^{th}} $ power of R. If the period of rotation of the particle is T, then: [JEE Main Online 08-04-2018]

Options:

A) $ T\propto {R^{(n+1)/2}} $

B) $ T\propto {R^{n/2}} $

C) $ T\propto {R^{3/2}} $ for any $ n $

D) $ T\propto {R^{\frac{n}{2}+1}} $

Show Answer

Answer:

Correct Answer: A

Solution:

  • For circular motion $ \frac{mv^{2}}{R}=\frac{c}{R^{n}} $
    $ \therefore v=\sqrt{\frac{c}{m{R^{n-1}}}} $
    $ \therefore TimeperiodT=( \frac{2\pi R}{v} ) $ $ T\propto {R^{( \frac{n+1}{2} )}} $