Question

A particle moves in circular path of radius $R$. If centripetal force $F$ is kept constant but the angular velocity is doubled, the new radius of the path will be

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

Answer 1

The correct option is C $\frac{R}{4}$

We know that , $F=m{\omega }^{2}R$

$\therefore R\propto \frac{1}{{\omega }^2}$ ($m$ and $F$ are constants)

If $\omega$ is doubled then radius will become $\frac{1}{4}$ times is i.e., $\frac{R}{4}$, where $R$ is the initial radius.

Hence option C is the correct answer