A rope passed over a pulley which is sufficiently high. Two monkeys climb the rope from the opposite ends, one of them climbing quickly than the other. Assuming that the pulley and the rope are weightless. Which monkey would reach the top first.
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Solution

Therefore, however quickly the monkeys move their paws up the rope, they will rise, relative to the ground, at equal rates, since they are of equal mass. And the rope will move through the pulley, to the side of the monkey which climbs the faster, with a velocity which will make the rates at which the monkeys climb, relative to the ground, equal. Therefore both monkeys will reach the pulley at the same time. The problem can be simplified so that the solution should be quite clear. Let us imagine that the monkeys are on an absolutely smooth horizontal surface and hold opposite ends of a rope. Since there are no external forces acting, the centre of gravity of the two monkeys must remain stationary and therefore they can only move equal distances towards this centreHof gravity, however fast either of them moves its paws along the rope. Therefore both monkeys will reach the point lying at the centre of the original distance between them simultaneously:

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A rope passed over a pulley which is sufficiently high. Two monkeys climb the rope from the opposite ends, one of them climbing quickly than the other. Assuming that the pulley and the rope are weightless. Which monkey would reach the top first. Please explain

A rope passed over a pulley which is sufficiently high. Two monkeys climb the rope from the opposite ends, one of them climbing quickly than the other. Assuming that the pulley and the rope are weightless. Which monkey would reach the top first.
Please explain