A bucket of mass ?m? is tied to a massless cable that is wrapped around the outer rim of a frictionless uniform pulley of radius R, similar to the system shown in Fig. E9.43. In terms of the stated variables, what must be the moment of inertia of the pulley so that it always has half as much kinetic energy as the bucket?

Solution 48E Kinetic energy of an object having moment of inertia I and angular velocity is given as, K = I 2 2 Given in the question that, I = 2 1 × ( × m × s ) , m is ths mass of the stone. 2 2 2 1 2 1 2 2I = 4 × 1.50 kg × v 2 1I × v = 1 × 1.50 kg × v , R is the radius of the pulley. 2 R2 4 I = 1 × 1.50 kg × R 2 2 2 I = 0.75R Thi is the required value of moment of inertia of the pulley.