Discussion Forum

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 

Answer:

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

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

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