Question

The monkey B shown in figure above is holding on to the tail of the monkey A who is climbing up an ideal rope. The masses of the 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 $g=10m/s^2$

• A. between 50 N and 80 N
• B. between 30 N and 80 N
• C. between 70 N and 105 N
• D. between 60 N and 90 N

Answer 1

Answer: (C)

between 70 N and 105 N

Given the monkey A can handle a maximum of 30 N of tension on its tail and a minimum of 20 N ( it has to carry the monkey B ).

Let the tension in its tail be 30 N, then acceleration of the monkey B which will be equal to the acceleration of monkey a.

$T-m_b\ast g=m_b\ast a$
$30-20=2\ast a$
$a=5m/s^2$

Now taking both the monkeys combined as a single body, we know the only external force is upward force applied by the rope and downward gravitational force or weight.
Maximum force is applied to the rope when the acceleration of the body is $5m/s^2$
Let the force applied by the rope be F then,

$F=(m_a+m_b)\ast (g+a)$

In case of max. acceleration,
$F=105$ N

In case of constant velocity i.e. zero acceleration,
$F=70N$