Consider the situation shown in the figure. All the surfaces are smooth. The tension in the string connected to $2m$ is

If the acceleration of $A$ is $2 \, m/s^2$ to the left and the acceleration of $B$ is $1 \, m/s^2$ to the left, then the acceleration of $C$ is

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:

If block $A$ is moving with an acceleration of $5\,m/s^2$,the acceleration of $B$ with respect to the ground is:

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?

Find the velocity of the hanging block if the velocities of the free ends of the rope are as indicated in the figure.