Calculate the acceleration of the block $B$ in the figure,assuming the surfaces and the pulleys $P_1$ and $P_2$ are all smooth and the pulleys and string are massless.

Two equal masses $A$ and $B$ are arranged as shown in the figure. The pulley and string are ideal and there is no friction. Block $A$ has a speed $u$ in the downward direction. The speed of the block $B$ is:

The boxes of masses $2\, {kg}$ and $8\, {kg}$ are connected by a massless string passing over smooth pulleys as shown in the figure. Calculate the time taken by the box of mass $8\, {kg}$ to strike the ground starting from rest. (Use $g = 10\, {m/s^2}$) (in ${s}$)

An iron rod of length $1.5 \,m$ lying on a horizontal table is pulled up from one end along a vertical line so as to move it with a constant velocity $3 \,m/s$, while the other end of the rod slides along the floor. After how much time will the speed of the end sliding on the floor equal the speed of the end being pulled up?

Two particles $A$ and $B$ are connected by a rigid rod $AB$. The rod slides along perpendicular rails as shown in the figure. The velocity of $A$ to the left is $10\; m/s$. What is the velocity of $B$ (in $m/s$) when the angle $\alpha = 60^{\circ}$?

At a given instant,block $A$ is moving with a velocity of $5\,m/s$ upwards. What is the velocity of block $B$ at that time?