Question

The monkey $B$, as 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 $5kg$ and $2kg$, respectively. If $A$ can tolerate a tension of $30N$ in its tail, find the range of the force that it can apply on the rope for it to carry monkey $B$ with it.
Take $g=10{m/s}^2$

• A. $20N$ to $100N$
• B. $35N$ to $100N$
• C. $50N$ to $105N$
• D. $70N$ to $105N$

Answer 1

The correct option is D $70N$ to $105N$

Let the acceleration of monkey $A$ and monkey B in vertically upward direction be $a$, so that a maximum tension of $30N$ is produced in the tail of monkey A.
$T-5g-30=5a$ ... (i)
$30-2g=2a$ ... (ii)
From equations (i) and (ii), we have:
$T=105N$ (max.)
and $a=5{m/s}^2$,which is acceleration of Monkey A= acceleration of monkey B (because both monkey are part of same system connected by tail of A)
So, $A$ can apply a maximum force of $105N$ on the rope to carry monkey $B$ with it.
For minimum force, there is no acceleration of $A$ and $B$.
$T_1=$ weight of monkey $B$
$\Rightarrow T_1=20N$
Rewriting equation (i) for monkey $A$, we get:
$T-5g-20=0$
$\Rightarrow T=70N$
$\therefore$ To carry monkey $B$ with it, monkey $A$ should apply a force of magnitude between $70N$ and $105N$.