In the figure shown, $A$ and $B$ are free to move, and they are released from rest. All the surfaces are smooth. $\left(0<\theta <90°\right)$

In the pulley system shown in the figure, the block $C$ is going up at $2 \mathrm{m} {\mathrm{s}}^{-1}$ and the block $B$ is going up at $4\mathrm{ }\mathrm{m} {\mathrm{s}}^{-1}$. Find the velocity of block $A$.

A system is shown in the figure. A man is pulling the rope from both sides with constant speed $u$. Find the speed of the block.

A rod $AB$ is shown in the figure. The end $A$ of the rod is fixed on the ground. Block is moving with velocity $\sqrt{3} \mathrm{m} {\mathrm{s}}^{-1}$ towards the right. The velocity of the end $B$ of the rod, when the rod makes an angle of $60°$ with the ground is

In the figure shown, find the value of $\text{θ}$ [assume string to be tight].

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