Answer
The total kinetic energy is $~~6.9~J$
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 use conservation of energy to find the total kinetic energy $K_2$ after the ball moves $1.0~m$ up the incline:
$K_2+U_2 = K_1+U_1$
$K_2 = K_1+0-U_2$
$K_2 = K_1-Mgh$
$K_2 = (20~J)-(2.67~kg)(9.8~m/s^2)(1.0~m)~sin~30^{\circ}$
$K_2 = 6.9~J$
The total kinetic energy is $~~6.9~J$
