Answer
$v = 3.0~m/s$
Work Step by Step
The rotational inertia of a hollow sphere is $I = \frac{2}{3}MR^2$
We can find the mass of the sphere:
$I = \frac{2}{3}MR^2 = 0.040~kg~m^2$
$M = \frac{(3)(0.040~kg~m^2)}{2R^2}$
$M = \frac{(3)(0.040~kg~m^2)}{(2)(0.15~m)^2}$
$M = 2.67~kg$
We can find an expression for the total kinetic energy:
$K = \frac{1}{2}Mv^2+\frac{1}{2}I\omega^2$
$K = \frac{1}{2}Mv^2+\frac{1}{2}(\frac{2}{3}MR^2)(\frac{v}{R})^2$
$K = \frac{1}{2}Mv^2+\frac{1}{3}Mv^2$
$K = \frac{5}{6}Mv^2$
We can find the speed of the center of mass at the initial position:
$K = \frac{5}{6}Mv^2 = 20~J$
$v^2 = \frac{(6)(20~J)}{5M}$
$v = \sqrt{\frac{(6)(20~J)}{5M}}$
$v = \sqrt{\frac{(6)(20~J)}{(5)(2.67~kg)}}$
$v = 3.0~m/s$
