Question

Two monkeys $(1)$ and $(2)$ of same mass $m=1kg$ are hanging on the strings such that the block of mass $2kg$ remains at rest. It is given that monkey $(2)$ is just holding the string. Find the acceleration (in $m/s^2$ ) of monkey $(1)$ with respect to his rope. (Take $g=10m/s^2$ )

Answer 1

Answer: 35

Mass $2kg$ is at rest,
so $T_2=20N$
So for $(2)$,
$T_2-mg=ma$
$20-10=1\times a$
$a=10m/s^2$
$T_1=2T_2=40N$
So for (1),
$T_2-mg=ma$
$40-10=1\times a$
$a=30m/s^2$
End of rope is coming down with $5m/s^2.$
So, acceleration of $(1)$ w.r.t. his rope is $30+5=35m/s^2$ upwards.
Acceleration of monkey $(2)$ with respect to his rope is zero because he is just holding the string.