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} )}} $
