In the figure shown the block $B$ moves down with a velocity $10 m/s$. The velocity of $A$ in the position shown is ......... $m/s$

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

A slider block $A$ moves downward at a speed of $v_A = 2\ m/s$ , at an angle of $75^o$ with horizontal as shown in the figure. The velocity with respect to $A$ of the portion of belt $B$ between ideal pulleys $C$ and $D$ is $v_{CD/A} = 2\ m/s$ at an angle $\theta $ with the horizontal. The magnitude of velocity of portion $CD$ of the belt when $\theta  = 15^o$ is   .......... $m/s$

In the figure, mass of a ball is $\frac{9}{5}$ times mass of the rod. Length of rod is $1 \,m$. The level of ball is same as rod level. Find out time taken by the ball to reach at upper end of rod. (in $S$)

In the figure shown the velocity of lift is $2\,m / s$ while string is winding on the motor shaft with velocity $2\,m / s$ and block $A$ is moving downwards with a velocity of $2\,m / s$, then find out the velocity of block $B -$

A block is dragged on a smooth plane with the help of a rope which moves with a velocity $v$ as shown in figure. The horizontal velocity of the block is