If $m_1 = 4m_2$,what is the acceleration of $m_2$? The acceleration of $m_1$ is $a$.

The pulleys in the diagram are all smooth and light. The acceleration of $A$ is $a$ upwards and the acceleration of $C$ is $f$ downwards. The acceleration of $B$ 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?

The velocity of end $A$ of a rigid rod placed between two smooth perpendicular walls moves with velocity $u$ along the vertical direction. Find the velocity of end $B$ of the rod,given that the rod always remains in contact with the walls.

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

$A$ basket and its contents have mass $M$. $A$ monkey of mass $2M$ grabs the other end of the rope and very quickly (almost instantaneously) accelerates by pulling hard on the rope until he is moving with a constant speed of $v_{m/r} = 2 \, ft/s$ measured relative to the rope. The monkey then continues climbing at this constant rate relative to the rope for $3 \, s$. How fast is the basket rising at the end of the $3 \, s$? Neglect the mass of the pulley and the rope. (given : $g = 32 \, ft/s^2$)