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

Answer 1

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

$F=m{v}^2/R$

$i.e.F\propto 1/R$

We know that if R is doubled, the force would be halved.
So, the centripetal force acting on the body would be $\frac{F}{2}$