Q67 / 90 · KVPY 2014 (SB/SX) · Physics

A body moves in a circular orbit of radius $\mathrm{R}$ under the action of a central force. Potential due to the central force is given by $V(r)=\operatorname{kr}(k$ is a positive constant). period of revolution of the body is proportional to :

Correct answer
A
$R^{1 / 2}$
B
$R^{-1 / 2}$
C
$R^{-3 / 2}$
D
$\mathrm{R}^{-5 / 2}$

Solution

$V(r)=k r$ $U(r)=m k r \quad \omega^{2}=\frac{k}{r}$ $\begin{aligned} F=-\frac{d u}{d r}=-m k \quad \omega=\sqrt{\frac{k}{r}} \\ & T=\frac{2 \pi \sqrt{r}}{\sqrt{k}} \end{aligned}$

Hence, the correct answer is option: 'A'.

More Rotational Motion Questions

A spherical rigid ball is released from rest and starts rolling down an inclined plane from height h = 7 m , as shown in the figure. It hits2019 (SB/SX)
A train is moving slowly at 2 m / s next to a railway platform. A man, 1 . 5 m tall, alights from the train such that his feet are fixed on 2019 (SB/SX)
A table has a heavy circular top of radius 1 m and mass 20 kg placed on four light (considered massless) legs placed symmetrically on its ci2018 (SB/SX)
Persons and are standing on the opposite sides of a wide water stream which they wish to cross. Each one of them has a rigid wooden plank wh19 Nov, 2017 (SA)
Two parallel discs are connected by a rigid rod of length centrally. Each disc has a slit oppositely placed as shown in the figure. A beam o19 Nov, 2017 (SA)
A uniform thin wooden plank AB of length and mass is kept on a table with its end slightly outside the edge of the table. When an impulse is19 Nov, 2017 (SB/SX)