In the arrangement shown,the mass $m$ will ascend with an acceleration (Pulley and rope are massless).

$A$ frictionless pulley is attached to one arm of a balance and a string passed around it carries two masses $m_1$ and $m_2$. The pulley is provided with a clamp due to which $m_1$ and $m_2$ do not move with respect to each other. On removing the clamp,if the counter mass restores balance,then the acceleration of the centre of mass of the masses $m_1$ and $m_2$ will have a magnitude of?

$250 \; N$ force is required to raise a $75 \; kg$ mass using a pulley system. If the rope is pulled by $12 \; m$ and the load is lifted by $3 \; m$,the efficiency of the pulley system will be ......$\%$

$A$ student calculates the acceleration of $m_1$ in the figure shown as $a_1 = \frac{(m_1 - m_2)g}{m_1 + m_2}$. Which assumption is not required to do this calculation?

$A$ uniform metal chain of mass $m$ and length $L$ passes over a massless and frictionless pulley. It is released from rest with a part of its length $l$ hanging on one side and the rest of its length $L - l$ hanging on the other side of the pulley. At a certain point in time,when $l = \frac{L}{x}$,the acceleration of the chain is $\frac{g}{2}$. The value of $x$ is ........

The system of two masses $2 \ kg$ and $3 \ kg$ as shown in the figure is released from rest. The work done on the $3 \ kg$ block by the force of gravity during the first $2 \ s$ of its motion is $\left(g=10 \ m/s^2\right)$. (in $J$)