In each of the three arrangements,the block of mass $m_1$ is being pulled left with constant velocity $v$. There is no friction anywhere. The strings are light and inextensible and pulleys are massless. The ratio of the speed of the block of mass $m_2$ in the three cases respectively is

In the pulley system shown in the figure,the mass of $A$ is half of that of $\text{rod } B$. The rod length is $500 \text{ cm}$. The mass of pulleys and the threads may be neglected. The mass $A$ is set at the same level as the lower end of the rod and then released. After releasing the mass $A$,it would reach the top end of the rod $B$ in time (Assume $g=10 \text{ m/s}^2$): (in $\text{ s}$)

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?

Blocks $A$ (mass $2m$),$B$ (mass $4m$),and $C$ (mass $m$) are arranged as shown in the figure. $A$ force $F$ is applied to block $A$. Find the acceleration of block $B$.

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 ............ $m/s^2$.

$A$ rod is constrained to move along a vertical wall and a horizontal floor. If the velocity of end $A$ is $V_A$ along the horizontal floor,find the velocity $V_B$ of end $B$ along the vertical wall in terms of $V_A$ and $\theta$.