Discussion Forum



1)

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 


A) $T\propto R^{\frac{3}{2}}$ For any n

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

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

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

Answer:

Option D

Explanation:

Force = Mass $\times$ Acceleration = $m\omega^{2}R$

and given ,  $ F\propto\frac{1}{R^{n}}\Rightarrow F=\frac{k}{R^{n}}$

 So, we have

     $\frac{k}{R^{n}}=m (\frac{2\pi}{r})^{2}\times R$

    $T^{2}=\frac{4\pi^{2}m}{k} R^{n+1} \Rightarrow T\propto R^{\frac{n+1}{2}}$