Q.
The monkey $B$ shown in figure is holding on to the tail of the monkey $A$ which is climbing up a 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 $g = 10\ ms^{- 2}$)
A) 105 N
B) 108 N
C) 10.5 N
D) 100 N
Explanation
(a) If $A$ is climbing with constant velocity, then
$T^{''} = 5g + T$ and $T = 2g$
$T^{''} = 5g + 2g = 7g = 7 \times 10$N=70N
Suppose $A$ is climbing with acceleration $a$ such that $T = 30$ N
That $T = 30$ N
$T - 2a = 2a$
$30 - 2 \times 10 = 2a$
or $a = 5\ ms^{- 2}$
Again, $T^{''} - T - 5g = 5a$ or $T^{''} = T + 5g + 5a$
or $T^{''} = (30 + 50 + 25)$ N= 105 N
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Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.