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.

The velocities of block $A$ and block $B$ are shown in the figure. The velocity of block $C$ is ......... $m/s$ (assume that the pulleys are ideal and the string is inextensible).

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?

$A$ block $Q$ of mass $M$ is placed on a horizontal frictionless surface $AB$ and a body $P$ of mass $m$ is released on its frictionless slope. As $P$ slides by a length $L$ on this slope of inclination $\theta$,the block $Q$ would slide by a distance:

If block $A$ has a velocity of $0.6\,m/s$ to the right,determine the velocity of block $B$.

The machine as shown has $2$ rods of length $1\, m$ connected by a pivot at the top. The end of one rod is connected to the floor by a stationary pivot and the end of the other rod has a roller that rolls along the floor in a slot. As the roller moves back and forth,a $2\, kg$ weight moves up and down. If the roller is moving towards the right at a constant speed,the weight moves up with a: