Two bodies of masses m₁=5 kg and m₂=3 kg are connected by a light string going over a smooth light pulley on a smooth inclined plane as shown in the figure. The system is at rest. The force exerted by the inclined plane on the body of mass m₁ will be : [Take g=10 ms⁻²]

Solution

Physics sir · 3 steps

The hanging block fixes the tension, the tension fixes the angle, and the angle gives the normal force.

1. Tension from m2. The system is at rest, so the hanging block is in balance: T = m₂ g = 3 × 10 = 30 N.
2. Find the angle. Along the smooth incline, only the string pulls m₁ up and only m₁ g sin θ pulls it down. So 50 sin θ = 30, which gives sin θ = 3/5 and cos θ = 4/5.

   N = m₁ g cos θ = 5 × 10 × 4/5 = 40 N

3. So. The plane is smooth, so it exerts no friction and its whole force on m₁ is the normal force, 40 N. That is option (b).

The idea to keep. When a system is at rest and the angle is not given, use the balance along the incline to find sin θ first. A smooth surface pushes only perpendicular to itself.

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