a uniform sphere rolls on a horizontal surface at 20m/s and then rolls up an incline that is inclined at 30 degrees to a height h from the ground.

if frictional forces are negligible , show that the height h is independent of the mass of the sphere hence calculate the value of h.

Hint: use \Delta KE + \Delta PE = 0. Remember that the kinetic energy of a rolling sphere has a component due to translation of \frac 1 2 m v^2 plus a component due to rotation of \frac 1 2 I \omega 2. Work this equation a bit and what do you find?