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 . Initialy th

Question

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 $μ$ . Initialy the system is at rest. A time varying horizontal force $F = 2 t$ 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 :-

TestHub · Accepted Answer

Till sliding starts the base stays at rest, so $F = 2 t$ only spins the disc: $τ = FR$ , $I = \frac{m R ^{2}}{2}$ ⇒ $α = \frac{4 t}{m R}$ , $ω = \frac{2 t ^{2}}{m R}$ .

Sliding begins when $F = μ (m + M) g$ ⇒ $t = \frac{μ ( m + M ) g}{2}$ .

$K E = \frac{1}{2} I ω^{2} = \frac{t ^{4}}{m} = \frac{1}{m} (\frac{μ ( m + M ) g}{2})^{4}$ - (B)

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