A pulley with a radius R=0.50m and a mass of M=4.0kg is mounted on a frictionless axle. The pulley is a uniform solid disk with rotational inertia I=1/2MR^2. A block with mass m=2.0kg hangs from a string wrapped around the pulley. When the system is released from rest the block accelerates down. Use g=10m/s^2.

a) After dropping through a height h, the block's speed is 2.0m/s. Using energy conservation, find h.

b) Apply Newton's Second Law and Newton's Second Law of Rotation. Solve your equations to find the acceleration of the block.

c) Use your value from (b) and one or more constant-acceleration equations to find h, the distance the block has dropped when its speed reaches 2.0m/s. Does it agree with your answer from (a)?