Two particles $A$ and $B$ are connected by a rigid rod $AB$. The rod slides along perpendicular rails as shown in the figure. The velocity of $A$ to the left is $10\; m/s$. What is the velocity of $B$ (in $m/s$) when the angle $\alpha = 60^{\circ}$?

$A$ 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 : $g = 32 \, ft/s^2$)

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

The velocities of block $A$ and block $B$ are shown in the figure. The velocity of block $C$ is ......... $m/s$ (assume that the pulleys are ideal and the string is inextensible).

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