A 2 kg brick begins to slide over a surface which is inclined at an angle of 45° with respect to horizontal axis. The co-efficient of static friction between their surfaces is:

Solution

Physics sir · 3 steps

Just begins to slide means friction is at its limit, so the angle of repose gives you μ directly.

1. Balance along incline. At the instant the brick starts to slide, static friction has reached its maximum value μₛ N. Along the incline, it just balances mg sin θ.
2. Balance across incline. Perpendicular to the incline there is no motion, so the normal force is N = mg cos θ.

   μₛ mg cos θ = mg sin θ ⇒ μₛ = tan θ

3. So. The mass cancels, so the 2 kg does not matter. With θ = 45°, μₛ = tan 45° = 1, which is option (a).

The idea to keep. When a block is just about to slide on an incline, μₛ = tan θ, where θ is the angle of repose. The mass never enters, so ignore it.

Answer from the NTA final answer key. Solution by PrepWiser.