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Question

The monkey B shown in the figure is holding onto the tail of the monkey A which is climbing up a rope. The masses of monkeys A and B are 5 kg and 2 kg respectively. If A can tolerate a tension of 30 N in its tail, what force should it apply on the rope in order to carry the monkey B with it ? (take g=10 m/s2)


A
T70 N and T85 N
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B
T60 N and T85 N
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C
T60 N and T105 N
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D
T70 N and T105 N
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Solution

The correct option is D T70 N and T105 N
Suppose A moves upward with acceleration a such that maximum tension 30 N is produced in its tail.


T5gT1=5a
T5g30=5a....(i)
T12g=2a
302g=2a(ii)

From equation (i) and (ii), we have
a=5 m/s2 and T=105 N (max)
So, A can apply a maximum force of 105 N on the rope to carry the monkey B with it.

For minimum force there is no acceleration of monkey A and B.
a=0

From equation (i),
T12g=0
T1=20 N (weight of monkey B)

From equation (ii),
T5g20=0 as T1=20 N
T=70 N

The monkey A should apply force between 70 N and 105 N to carry monkey B with it.

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