A physics question?

Question

What is the final angular velocity in unit of rad/sec of a solid sphere with radius of 8.55 meters rolls down without slipping a hill of 66.81 meter height, starting from rest? Use g = 9.8 m/s2. The moment of inertia of the solid sphere is 2/5*MR2.

Answer 1

PE = KE_linear + KE_rotational

Answer 2

PE = m*g*h = KEt+KEr 

KEt = m/2*V^2

KEr = m/5*V^2

KE = KEt+KER = 0.7m*V^2 = m*g*h (conservation of energy) 

V = √ g*h/0.70 = √ 9.80*66.81*1.429 = 30.6 m/sec