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The monkey-on-a-rope question tests one idea: tension depends on acceleration, not on which way the monkey is moving. Students who think "climbing up means more tension" get half the cases right and half wrong. This post sets up one equation, runs it through six cases with numbers, then adds a rope that can break and a rope that has mass.
Is this on the syllabus?
Yes. The JEE (Main) 2026 syllabus and the NEET (UG) 2026 syllabus both list Newton's laws of motion, momentum and the second law under Laws of Motion. The NCERT Class 11 chapter Laws of Motion (2026-27 reprint) does not have a monkey exercise, but its Exercise 4.13, a man on a weighing scale in a lift, is the same physics. Its summary points also warn that mg and the normal force are equal only in equilibrium, which is the heart of this problem too. Check the syllabus for your exam year.
What forces act on the monkey?
Draw the monkey alone. Two forces act on it:
its weight mg, downwards;
the tension T from the rope, upwards, at its hands.
The monkey grips and pulls down on the rope; by Newton's third law the rope pulls up on the monkey with the same force. That upward pull is the only thing that can make the monkey speed up going up. Take up as positive:
T − mg = ma, so T = m(g + a)
Here a is the monkey's acceleration, positive if it points up and negative if it points down. For a refresher on drawing the diagram first, see our guide to Newton's second law and free-body diagrams.
Six cases, worked with numbers
Take a 20 kg monkey and g = 9.8 m/s² (sample numbers). Then mg = 196 N.
Climbing up, speeding up at 2 m/s². a = +2. T = 20 × 11.8 = 236 N.
Climbing up at a steady speed. a = 0. T = 196 N. Any constant speed, up or down, gives the same answer.
Climbing up, slowing down at 3 m/s². The acceleration points down: a = −3. T = 20 × 6.8 = 136 N.
Sliding down, speeding up at 3 m/s². Again acceleration points down: a = −3. T = 136 N, the same as case 3.
Sliding down, slowing down at 3 m/s². Now the acceleration points up: a = +3. T = 20 × 12.8 = 256 N, the largest tension so far, even though the monkey is moving down.
Letting go and falling freely. a = −9.8. T = 0.
Cases 3 and 4 look opposite but give the same tension. Cases 1 and 5 look opposite but both raise the tension above mg.
When does the rope break?
Suppose the rope can take at most 300 N. Set T = 300: 300 = 20(9.8 + a), so a = 5.2 m/s². The rope breaks if the monkey's acceleration points up and exceeds 5.2 m/s², either by climbing faster too quickly or by braking too hard on the way down. Any downward acceleration is safe, because it lowers the tension.
This is how exam questions usually phrase it: four motions, pick the ones that snap the rope. Work out a for each with its sign, and compare m(g + a) with the limit.
What if the rope has mass?
Hang a 2 kg rope from a ceiling hook and let the monkey from case 1 climb it. The rope itself does not accelerate, so the hook must hold up the rope's weight plus the 236 N the monkey pulls with:
T(top) = 236 + 2 × 9.8 = 255.6 N
The tension then varies along the rope. Our post on tension in a heavy rope shows how it changes with height.
Which mistakes cost marks?
Deciding by velocity. "Moving down means less tension" fails in case 5.
Signing a by the word "slowing". Slowing down only tells you a is opposite to v. Work out the direction, then the sign.
Putting ma on the force side as a force. In the ground frame there are only two forces, T and mg.
Forgetting the rope's own weight at the top of a heavy rope.
Mixing g = 9.8 and g = 10 in one problem. Use what the question gives.
If you can set up the equation but keep choosing the wrong sign, the Fermi Problem Library has worked problems with a step-by-step solver that explains the reasoning, so you can see where the sign choice is made.
A practice routine
Day 1: Do NCERT Exercise 4.13 (the lift) and then rewrite each part as a monkey on a rope. Check that the answers match.
Day 2: Make your own table of eight motions (up or down, speeding up, slowing down or steady) and write the sign of a for each.
Day 3: Three breaking-rope questions with different limits.
Day 4: Two heavy-rope questions, then a lift question from our post on relative motion in a lift.
Tonight, find the tension when a 15 kg monkey slides down and slows at 2 m/s², and say in one sentence why it is more than its weight.
