The monkey B shown in figure is holding on to the tall of the monkey A which is climbing up a rope. The masses of the monkeys A and B are 5 kg and 2kg 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/s^2`.

Explanation

Suppose A moves upward with acceleration a such that in the tail of a maximum tension 30 N produced.
`T-5g-30-5a=0`…..i ltbRgt `30-2g-2a=0` …….ii.
Form equation i. and ii, we have
`rarr T=105 N (max.)`
and `a=5 m/s^2`
So, A can apply a maximum forc eof 105 N in the rope to carry the monkey B with it.
For minimum force there is no acceleration of monkey A and B.
`rarr a=0`
From equation ii,
`T_1 -2g=0`
`rarr T_1 = 20 N` (weight of monkey B)
From equation i.
` T-5g-20=0`
`as T_1 =20`
`rarr T-5g-20=0`
` T=70N`
`:.` The monkey A should apply force betwen 70 N and 105 N to carry the monkey B with it.