Consider a wedge of mass 2m and a cube of mass m . Between the cube and wedge, there is no friction. The minimum coefficient of friction between the wedge and the ground so that the wedge doesn’t move is

The coefficient of friction is represented as μ. The frictional force is divided into horizontal and vertical components. Those are λsinθ and λcosθ.

⇒ λsinθ = Fr

⇒ λsinθ = μ ( 2mg + mgcos2θ)

⇒ mgsinθcosθ = μ (2mg+mgcos2θ)

⇒ 12 = μ(2 + 1/2)

⇒ 12 = μ(5/2)

⇒ μ = 1/5

∴ μ = 0.5

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