$A$ light string passing over a smooth light pulley connects two blocks of masses $m_1$ and $m_2$ (where $m_2 > m_1$). If the acceleration of the system is $\frac{g}{\sqrt{2}}$,then the ratio of the masses $\frac{m_1}{m_2}$ is:

Three blocks of mass $5 \ kg$ each are suspended from a ceiling as shown in the figure. The value of $\frac{T_3}{T_1}$ is .............

$A$ block of mass $25 \; kg$ is raised by a $50 \; kg$ man in two different ways as shown in the figure. What is the action on the floor by the man in the two cases? If the floor yields to a normal force of $700 \; N$,which mode should the man adopt to lift the block without the floor yielding?

In the figure,the tension in the diagonal string is $60\,N$. Find the magnitude of the horizontal forces $F_1$ and $F_3$ that must be applied to hold the system in the position shown.

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?