JEE Main 2023 · 31 January · morning · Single correct · +4 / −1
As shown in figure, a 70 kg garden roller is pushed with a force of F⃗=200 N at an angle of 30° with horizontal. The normal reaction on the roller is
(Given g=10 m s⁻²)
- (a) 800 N
- (b) 600 N
- (c) 200√3 N
- (d) 800√2 N
Answer and solution
Answer (a) 800 N
Solution
Physics sir · 4 steps
The push points downward into the ground, so its vertical part adds to the weight.
- Read the figure. The force F⃗ acts along the handle toward the centre of the roller. It slopes down at 30° below the horizontal.
- Split the force. Vertical part: F sin 30° = 200 × 1/2 = 100 N, pointing down. The horizontal part F cos 30° only pushes the roller along the ground and does not affect the normal reaction.
- Balance vertically. The roller does not move up or down, so the upward normal reaction balances the weight mg = 70 × 10 = 700 N plus the downward part of the push.
N = mg + F sin 30° = 700 + 100 = 800 N
- So. The normal reaction on the roller is 800 N, option (a).
The idea to keep. Pushing at an angle presses the body into the floor and raises N. Pulling at an angle lifts it and lowers N. Always check which way the vertical component points.
Answer from the NTA final answer key. Solution by PrepWiser.