In the figure shown,the velocity of the lift is $2\,m/s$ upwards. The string is winding on the motor shaft with a velocity of $2\,m/s$ and block $A$ is moving downwards with a velocity of $2\,m/s$ relative to the lift. Find the velocity of block $B$ with respect to the ground.

Block $B$ moves to the right with a constant velocity $v_0$. The velocity of body $A$ relative to $B$ is:

If the pulleys shown in the diagram are smooth and massless,and $a_1$ and $a_2$ are the accelerations of the blocks of mass $4 \, kg$ and $8 \, kg$ respectively,then:

In the given figure,the acceleration of wedge $A$ is $10 \ m/s^2$ along the inclined plane. There is no friction between $A$ and $B$,and between $A$ and the fixed inclined plane. Then the acceleration of block $B$ will be ............ $m/s^2$.

$A$ thin uniform rod of length $L$ is resting against a wall and the floor as shown in the figure. Its lower end $A$ is pulled towards the left with a constant velocity $v$. Then the downward velocity $v^{\prime}$ of the other end $B$ when the rod makes an angle $\theta$ with the floor 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: