Question

Two monkeys $M_{1}$ and $M_{2}$ of equal mass ' $m$ ' can climb strings of a pulley arrangement as shown in figure. Find magnitude of acceleration (in $m / s ^{2}$ ) of $M_{1}$ with respect to rope so that block remains stationary. It is given that $M_{2}$ is just holding the string. Assume pulley is frictionless and string is massless and inextensible.

Answer 1

$T=5\, m g$
$a_{2}=\frac{5 m g-m g}{m}=4\, g$
$T'=2 T=10\, mg$
$a_{1}=\frac{10 m g-m g}{m}=9\, g$
Acceleration of the rope is equal to the acceleration of the moving pulley.
Hence acceleration of $M_{1}$ with respect to rope
$a_{M_{1}, \text{Rope} }=9\, g-(-2 g)=11\, g=110\, m / s ^{2}$