Three blocks of masses $m_1=4 \, kg$, $m_2=2 \, kg$, and $m_3=4 \, kg$ are connected with ideal strings passing over a smooth, massless pulley as shown in the figure. The acceleration of the blocks will be ......... $m/s^2$ $(g=10 \, m/s^2)$.

$A$ particle of small mass $m$ is joined to a very heavy body of mass $M$ by a light string passing over a light pulley. Both bodies are free to move. The total downward force on the pulley is

The pulleys and strings shown in the figure are smooth and of negligible mass. For the system to remain in equilibrium,the angle $\theta$ should be:

$A$ 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?

$A$ 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,$m_1$ and $m_2$ start moving. How much change in counter mass has to be made to restore balance?

In the arrangement shown in the figure, the work done by the string on the block of mass $0.36 \,kg$ during the first second after the blocks are released from a state of rest is: (Ignore friction and the mass of the string.)
(Acceleration due to gravity, $g = 10 \,m/s^2$) (in $\,J$)