Two masses of size m and 4m are connected by a massless thread and are strung over a frictionless pulley of radius R and moment-of-inertia I. The two masses are held motionless at the same height and then released from rest. After the mass 4m has fallen a distance L and the mass m has risen the same distance L, what is the total kinetic energy of the entire system

Total kinetic energy of entire system is 3 mgl

Explanation:

Given two masses: m and 4m.

Since the pulley is frictionless and the thread is massless, the energy here is linked to the two masses.

Total kinetic energy of entire system = decrease in gravitational potential energy of the system.

Therefore, we have:

ΔKE = Δp

ΔKE = 4mgl - mgl

= 3 mgl

Total kinetic energy of entire system is 3 mgl