Answer
(a) $F_c=0.19N$
(b) If the speed doubles, the centripetal force will increase by $4$ times.
Work Step by Step
a) The mass of the ball $m=0.012kg$, the radius of the circle $r=0.1m$ and the rotation period $T=0.5s$
To find $F_c$, we can use the formula $$F_c=\frac{mv^2}{r}$$
Since $v$ can be written into $\frac{2\pi r}{T}$, we have $$F_c=\frac{m}{r}\times\frac{4\pi^2r^2}{T^2}=\frac{4\pi^2mr}{T^2}$$
Using the given information, we get $F_c=0.19N$
b) From the formula $F_c=\frac{mv^2}{r}$, we see that if $v$ is doubled, $F_c$ will increase by $2^2=4$ times.
