Question

In the system shown M = 10 kg. The coefficient of friction between block and ground is 0.4 and that between two blocks is 0.1. The maximum value of m (in kg) so that the arrangement shown in the figure is in equilibrium is given by p/4. Find the value of p.

Answer 1

p = 10

Answer 2

The pulley arrangement exerts a net horizontal pull of 2T on the big block M, where T = m g. For M to remain at rest on the rough horizontal surface, the friction force available must balance this pull. Assuming that m lies entirely on M so that the normal reaction from the ground is (M + m)g, the maximum friction force is   F₍max₎ = μ₁ (M + m)g = 0.4 (10 + m) g. Equating the forces for the limiting equilibrium condition gives   2 m g = 0.4 (10 + m) g. Cancelling g and solving:   2m = 4 + 0.4m ⟹ 2m – 0.4m = 4 ⟹ 1.6m = 4 ⟹ m = 2.5 kg. Since the maximum m is expressed as p/4, we have:   p/4 = 2.5 ⟹ p = 10.