$A$ 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?

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 ........... $N$.

Two masses $m_1$ and $m_2$ are connected by a light string passing over a smooth pulley. When set free,$m_1$ moves downwards by $3 \ m$ in $3 \ s$. The ratio of $\frac{m_1}{m_2}$ is $(g = 10 \ ms^{-2})$.

One end of a massless rope,which passes over a massless and frictionless pulley $P$,is tied to a hook while the other is free. The maximum tension the rope can bear is $360 \ N$. With what value of maximum safe acceleration (in $m \ s^{-2}$) can a man of $60 \ kg$ climb on the rope?

Two masses of $5\, kg$ and $3\, kg$ are suspended with the help of massless inextensible strings as shown in the figure. The whole system is moving upwards with an acceleration of $2\, ms^{-2}$. The tensions $T_1$ and $T_2$ are respectively (Take $g = 10\, ms^{-2}$)

In the pulley system shown,the mass of the ball is $1.2$ times greater than the mass of the rod. The length of the rod is $50 \,cm$. The ball is set on the same level as the lower end of the rod and then released. What is the acceleration of the rod with which it comes down (in $\,m/s^2$)? Assume the pulleys and threads are massless and friction is neglected. (Use $g = 10 \,m/s^2$)