Two masses $m_1 = 3\,kg$ and $m_2 = 7\,kg$ are tied to a string and are hanging over a light frictionless pulley. What is the acceleration of the masses when the system is free to move (in $,m/s^2$)? $[g = 10\,m/s^2]$

$A$ monkey of mass $50\,kg$ climbs on a rope which can withstand the tension $(T)$ of $350\,N$. If the monkey initially climbs down with an acceleration of $4\,m/s^2$ and then climbs up with an acceleration of $5\,m/s^2$,choose the correct option $(g = 10\,m/s^2)$.

Three equal weights $A, B$ and $C$ of mass $2\, kg$ each are hanging on a string passing over a fixed frictionless pulley as shown in the figure. The tension in the string connecting weights $B$ and $C$ is ........... $N$.

One end of a light string is fixed to a clamp on the ground and the other end passes over a fixed frictionless pulley as shown in the figure. It makes an angle of $30^{\circ}$ with the ground. The clamp can tolerate a vertical force of $40 \,N$. If a monkey of mass $5 \,kg$ were to climb up the rope,then the maximum acceleration in the upward direction with which it can climb safely is $\left(g=10 \,ms^{-2}\right)$ (in $\,ms^{-2}$)

Two masses $8\; kg$ and $12\; kg$ are connected at the two ends of a light inextensible string that goes over a frictionless pulley. Find the acceleration of the masses and the tension in the string when the masses are released.

$A$ pulley fixed to the ceiling carries a string with blocks of mass $m$ and $3m$ attached to its ends. The masses of the string and pulley are negligible. When the system is released,what is the acceleration of its centre of mass?