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:

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?

$A$ 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

For the given diagram,when block $B$ is pulled with velocity $V$,the velocity of block $A$ will be:

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

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