Question

Fc=mv2/r
Fc is centripetal force, m is mass, v is speed and r is radius


What will happen to the size of the centripetal force if the radius (r) is doubled?


1)No change
2)The centripetal force doubles
3)The centripetal force increases by a factor of 4
4)The centripetal force is halved

Answer 1

Let the old centripetal force be $F_c = \frac{m v^2}{r}$. When the radius is doubled, the new centripetal force is $F_c' = \frac{m v^2}{2 r}$. Dividing the new force by the old, obtain $\frac{F_c'}{F_c} = \frac{r}{2 r} = \frac{1}{2}$, so $F_c' = \frac{F_c}{2}$ - the centripetal force is halved.

The answer is 4).