A rod can freely rotate in the vertical plane about the hinge at its bottom. Two strings tie the top of the rod with blocks $A$ and $B$ as shown in the figure. At the instant shown, the rod is vertical and the speed of the block $A$ is $u \mathrm{m} {\mathrm{s}}^{-1}$ Find the speed of block $B.$

 A lift is moving upwards with a constant speed of  $5\mathrm{ }\mathrm{m} {\mathrm{s}}^{-1}$. The speed of one of the pulleys is $5\mathrm{ }\mathrm{m} {\mathrm{s}}^{-1}$ as shown in figure. Then, the speed of second pulley is,

In the figure shown, neglecting friction and mass of pulleys, what is the acceleration of mass $B$?

Two blocks of masses $m_1$ and $m_2$ are connected as shown in the figure. The acceleration of the block $m_2$ is

A system is shown in the figure. The velocity of sphere $A$ is $9 \mathrm{m} {\mathrm{s}}^{-1}$. Find the speed of sphere $B$.

In the given arrangement, the mass of the block is $M$ and the surface on which the block is placed is smooth. Assuming all pulleys to be massless and frictionless, strings to be inelastic and light, $R_1, R_2$ and $R_3$ to be light supporting rods, then, the acceleration of point $P$ will be ($A$ is fixed),

In the given arrangement, mass of the block is $M$ and the surface on which the block is placed is smooth. Assuming all pulleys to be massless and frictionless, strings to be inelastic and light, $R_1, R_2$ and $R_3$ to be light supporting rods, then, find the magnitude of the net force exerted by the pulley on the rod $R_1$.

The figure shows two blocks $A$ and $B$ connected to an ideal pulley string system. In this system, when the bodies are released, then (neglect friction and take $g=10 \mathrm{m} {\mathrm{s}}^{-2}$)