5. [10] A block of mass m hangs from a thread that is wound around a solid disk of mass M and radius R. The block is released from rest.

It picks up speed with a constant acceleration as it falls. While it falls the disk spins without friction, and the string does not slip. After falling a distance of 40 cm the speed of the block is 1.6 m/s. Starting with the conservation of mechanical energy principle, (U + K); = (U + K)†,calculate the ratio of the disk's mass to the block's mass, M/m. Show all the steps in your work and give a numerical answer.