A smooth circular groove has a smooth vertical wall as shown in figure. A block of mass m moves against the wall with a speed v. Which of the following curve represents the correct relation between the normal reaction on the block by the wall (N) and speed of the block (v) ?

Solution

Physics sir · 4 steps

The wall is the only thing pushing the block inward, so the wall alone supplies mv²/R.

1. Sort the forces. Vertically, gravity mg is balanced by the floor's normal force, and neither depends on speed. Horizontally, the smooth wall pushes the block towards the centre of the circle, and nothing else acts sideways because there is no friction.
2. Wall gives centripetal force. The block moves in a circle of radius R, so it needs a net inward force mv²/R. The wall's normal reaction N is the only inward force, so it must equal this.

   N = mv²/R ⇒ N ∝ v²

3. Shape of the graph. N ∝ v² is a parabola through the origin. It is flat near v = 0 and curves upward more and more steeply as v grows.
4. So. The upward-opening parabola starting at the origin, option (a), is the correct N versus v curve.

The idea to keep. In circular motion, find the force that points towards the centre. That force equals mv²/R, so it grows as v², never as v.

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