A wheel of the radius 0 . 4 m can rotate freely about its axis. A string is wrapped over its rim and a mass of 4 kg is hung. An angular acceleration of 8 rad s - 2 is produced in it due to the torque. Then, the moment of inertia of the wheel is ( g = 10 m s - 2 )

Step-by-step solution

Given, r = 0 . 4   m , α = 8  rad  s - 2 m = 4   kg , I   = ? Torque, τ = I α ⇒ mgr = I α or 4 × 1 0 × 0.4 = I × 8 ⇒ I = 16 8 = 2   kg   m 2 Or I = 2   kg m 2