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 $J$)

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 $,m/s^2$)? $[g = 10\,m/s^2]$

$A$ light unstretchable string passing over a smooth light pulley connects two blocks of masses $m_1$ and $m_2$. If the acceleration of the system is $\frac{g}{8}$,then the ratio of the masses $\frac{m_2}{m_1}$ is:

For the system shown in the figure,$m_1 > m_2 > m_3 > m_4$. Initially,the system is at rest in equilibrium. If the string joining $m_4$ and the ground is cut,then just after the string is cut:
Statement $I$: $m_1$,$m_2$,and $m_3$ remain stationary.
Statement $II$: The value of acceleration of all the $4$ blocks can be determined.
Statement $III$: Only $m_4$ remains stationary.
Statement $IV$: Only $m_4$ accelerates.
Statement $V$: All the four blocks remain stationary.
Now,choose the correct option.

Two identical masses $m$ are connected to a massless string which is hung over two frictionless pulleys as shown in the figure. If everything is at rest,what is the tension in the cord?

If $m_1 = 4m_2$ and the acceleration of $m_1$ is $a$,find the tension $T$ in the string.