Question

Two monkeys $(1)$ and $(2)$ of same mass $m=1 \,kg$ are hanging on the strings such that the block of mass $2\, kg$ 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 $g=10\, m / s ^{2}$ )

Answer 1

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