Question

A monkey of mass 40 kg climbs on a rope which can stand a maximum tension of 600 N. In which of the following cases will the rope break: the monkey (a) climbs up with an acceleration of 6 m/s2 (b) climbs down with an acceleration of 4 m/s2 (c) climbs up with a uniform speed of 5 m/s (d) falls down the rope nearly freely under gravity?

Answer 1

Tension in rope when monkey

1. Climbs up with acceleration of 6m/s^2
T = m (g + a) = 40 (10 + 6) = 640 N

2. Climbs down with an acceleration of 6 m/s^2
T = m (g - a) = 40 * (10 - 6) = 160 N

In case-1 tension in rope is 640 N which is greater than maximum tension of rope. Hence rope will break if monkey climbs up with acceleration of 6m/s^2.
Correct option is (a)

Answer 2

(a) Climbs up with acceleration of 6m/s^:
T - mg =ma
T= 40(10+6)
T= 640N
But given it can withstand only 600N. Therefore the rope breaks in this case.
Correct option is (a)
Detailed solution is in the attachment.

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