Two masses of $5 \ kg$ and $10 \ kg$ are suspended from a massless pulley as shown in the figure. Calculate the acceleration of the system when the masses are left free.

$A$ lift is tied with thick iron ropes having mass $M$. The maximum acceleration of the lift is $a \ m/s^2$ and the maximum safe stress is $S \ N/m^2$. The minimum diameter of the rope is

Two unequal masses are connected on two sides of a light string passing over a light and smooth pulley as shown in the figure. The system is released from rest. The larger mass $(2\, kg)$ is stopped $1\, s$ after the system is set into motion and then released. Find the time elapsed before the string becomes tight again. (Take $g = 10\, m/s^2$)

$A$ monkey of mass $40 \,kg$ climbs up a rope,of breaking load $600 \,N$ hanging from a ceiling. If it climbs up the rope with the maximum possible acceleration,then the time taken by the monkey to climb up is .........$s$ [Length of rope is $10 \,m$]

In the arrangement shown in the figure,the pulley is smooth and massless,and all the strings are light. Let $F_1$ be the force exerted on the pulley in case $(i)$ and $F_2$ be the force in case $(ii)$. Then:

The ends of a rope are held by two men who pull on it with equal and opposite forces of magnitude $F$ each. Then the tension in the rope is