Question

A particle moving along a circular path with the uniform angular velocity $\omega$ is under the action of a force 'F' directed towards the centre of the circular path. If the radius of the circular path is doubled without changing the linear velocity, the centripetal force acting on the body would be _____ .

• A. $\frac{F}{8}$
• B. F
• C. $\frac{F}{4}$
• D. $\frac{F}{2}$

Answer 1

The correct option is D $\frac{F}{2}$

Centripetal Force, $F=mr{\omega }^2$

where, $\omega =\frac{v}{r}$

If the radius is doubled, ${\omega }^{\prime }=\frac{v}{r^{\prime }}=\frac{v}{2r}=\frac{\omega }{2}$

and, $F^{\prime }=m{r}^{\prime }{\omega }^{\prime 2}=m2r\frac{{\omega }^2}{4}=\frac{1}{2}mr{\omega }^2=\frac{F}{2}$