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Question

The monkey B, shown in the following figure, is holding on to the tail of monkey A that 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 monkey B with it? (Take g=10 m/s2)

A
Between 50 N and 80 N
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B
Between 30 N and 80 N
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C
Between 70 N and 105 N
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D
Between 60 N and 90 N
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Solution

The correct option is C Between 70 N and 105 N
Let the acceleration of monkey A upwards be a so that a maximum tension of 30 N is produced in its tail.


T5gT15a=0.......(i)
T5g305a=0


From equation (i) and (ii), we have


T12g2a=0.......(ii)
302g2a=0
a=5 m/s2
So, putting (a=5 m/s2) in equation (i)
we get that A can apply a maximum force of 105 N on the rope to carry monkey B, hence Fmax=105 N

Now for the minimum force, monkey A can carry monkey B with constant velocity. So, a=0
From equation (ii)

T1=20 N
Rewriting equation (i) for monkey A, we get:
T5g20=0T=70 N

To carry monkey B with it, monkey A should apply a force of magnitude between 70 N and 105 N

Hence option C is the correct answer




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