Question

A particle of mass $9kg$ is moving under the action of a central force whose potential energy is given by $U=10/r$. For what energy it will orbit a circle of radius $10m$? Calculate the time period of this motion.

Answer 1

$U=\frac{10}{v}$ $E=\frac{10}{10}=1J$

Centripetal force -

$\Rightarrow \left|f\right|=\left|\frac{-du}{dr}\right|=+\frac{10}{r^2}$

Now, centripetal force $=$ centrifugal force

$\Rightarrow \frac{10}{r^2}=\frac{m{v}^2}{r}$

$v^2=\frac{10}{10\times 9}>\frac{1}{9}$

$v=\frac{1}{3}m/s$

$\Rightarrow T=\frac{2\pi v}{v}=\frac{2\pi \times 10}{1}3=60\pi sec$

Hence, the answer is $60\pi sec.$