Question

The radius of the circular path of a particle is doubled but its frequency of rotation is kept constant. If the initial centripetal force be $F$, then the final value of centripetal force will be:

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

Answer 1

Answer: (D)

$2F$

Frequency is constant, thus its angular velocity is constant $w=2\pi f$

Initial centripetal force $F=m{r}_1{w}_1^2$

But radius is doubled $r_2=2r_1$

$\therefore$ New centripetal force $F_2=m{r}_2{w}^2=m\left(2r_1\right)w^2=2F$