JEE Main 2022 · 26 July · morning · Single correct · +4 / −1
A monkey of mass 50 kg climbs on a rope which can withstand the tension (T) of 350 N. If monkey initially climbs down with an acceleration of 4 m / s² and then climbs up with an acceleration of 5 m / s². Choose the correct option (g=10 m / s²).
- (a) T=700 N while climbing upward
- (b) T=350 N while going downward
- (c) Rope will break while climbing upward
- (d) Rope will break while going downward
Answer and solution
Answer (c) Rope will break while climbing upward
Solution
Physics sir · 4 steps
Climbing up, the rope must hold the weight and push the extra acceleration. Compare that with 350 N.
- Forces on monkey. Only two forces act on the monkey: the rope pulls up with T and gravity pulls down with mg = 50 × 10 = 500 N. Take upward as positive and apply T - mg = ma.
T = m(g + a)
- Going down. The acceleration is downward, so a = -4 m s⁻². Then T = 50(10 - 4) = 300 N, which is less than 350 N. The rope holds.
- Going up. The acceleration is upward, so a = +5 m s⁻². Then T = 50(10 + 5) = 750 N, which is more than 350 N.
- So. The rope would need to supply 750 N but can only take 350 N, so the rope breaks while the monkey climbs upward. That is option (c).
The idea to keep. For anything hanging on a rope, tension is m(g + a) with upward acceleration and m(g - a) with downward acceleration. Accelerating up always strains the rope more than standing still.
Answer from the NTA final answer key. Solution by PrepWiser.