A block of mass M slides down on a rough inclined plane with constant velocity. The angle made by the incline plane with horizontal is θ. The magnitude of the contact force will be :

Solution

Physics sir · 3 steps

Constant velocity means zero net force, so the incline's total push must exactly cancel the weight.

1. Only two agents. Only two things act on the block: the Earth pulls with weight Mg, and the incline pushes. The incline's push has two parts, the normal force N and the friction f, and together they make the contact force.
2. Balance the forces. The velocity is constant, so the acceleration is zero and the net force is zero. Along the incline, f = Mg sin θ. Perpendicular to it, N = Mg cos θ.

   F_(contact) = √(N² + f²) = √((Mg cos θ)² + (Mg sin θ)²) = Mg

3. So. The contact force has magnitude Mg and points straight up, opposite to the weight. The answer is (a).

The idea to keep. Contact force means normal plus friction together. If a body moves with constant velocity under only weight and contact, the contact force must equal Mg and point vertically up.

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