A wheel (disc of mass m, radius R) is mounted on a base of mass M. The whole system is placed on rough horizontal surface. The coefficient of friction between the base & the surface is μ. Initially the system is at rest. A time varying horizontal force F = 2t is applied tangentially on the wheel, where t is time in second & force F is in newton. The kinetic energy of the disc when the system is about to slide on ground is:-

Question

G1 Physics · Accepted Answer

The base begins to slide when the required ground friction reaches µ(m+M)g. Use τ = FR for the disc, α = τ/I and integrate F=2t from rest to the limiting time. The resulting kinetic energy is (1/m)[µ(m+M)g/2]⁴. Hence B.