Question

Two masses M1 and M2 are connected by a light rod and the system is slipping down a rough incline of angle θ with the horizontal. The friction coefficient at both the contacts is µ. Find the acceleration of the system and the force by the rod on one of the blocks.

Answer 1

Let the Force which the Rod will apply on the Block of mass M₁ block be F.

For Block M₁,

M₁gSinθ - μM₁gCosθ + F = M₁a

⇒ a = g(Sinθ - μCosθ) + F/M₁

For Block M₂,

a = g(Sinθ - μCosθ) - F/M₂

Since, the system contains two blocks which are joined by same String, therefore, there individual acceleration will be same.

∴ g(Sinθ - μCosθ) - F/M₂ = g(Sinθ - μCosθ) + F/M₁

⇒  F/M₁ +  F/M₂ = 0

∴ F = 0

∴ The Force applied by the Rod on the block will be zero.

∴ Acceleration of the System = g(Sinθ - μCosθ)

Hope it helps.