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Question

A rope which can withstand a maximum tension of 400 N is hanging from a tree. If a monkey of mass 30 kg climbs up the rope, in which of the following cases will the rope break? Take g=10ms−2 and neglect the mass of the rope.


A

The monkey climbs up with a uniform speed of 5 ms1.

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B

The monkey climbs up with a uniform acceleration of 2 ms2.

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C

The monkey climbs up with a uniform acceleration of 5 ms2.

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D

The monkey climbs down with a uniform acceleration of 5 ms2.

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Solution

The correct option is C

The monkey climbs up with a uniform acceleration of 5 ms2.


Mass of monkey, m=30 kg
Acceleration due to gravity, g=10 ms2
If the monkey climbs up the rope with a uniform acceleration a, the tension in the rope is T = m(g + a). If he climbs down with a uniform acceleration a, the tension is T = m(g - a).
In case (a), since the speed is uniform, a = 0. Therefore, T=mg=30×10=300 N
In case (b), the tension is given by T=m(g+a)=30×(10+2)=360 N
In case (c), the tension is given by T=m(g+a)=30×(10+5)=450 N
In case (d), the tension is given by T=m(ga)=30×(105)=150 N
Since the rope can withstand a maximum tension of 400 N, the rope will break only in case (c). Hence, the correct choice is (c).


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