Find the velocity of the hanging block if the velocities of the free ends of the rope are as indicated in the figure.
$\frac{3}{2}\,m / s \uparrow$
$\frac{3}{2}\,m / s \downarrow$
$\frac{1}{2}\,m / s \uparrow$
$\frac{1}{2}\,m / s \downarrow$
A block of mass $M$ is tied to one end of massless rope. The other end of rope is in the hands of a man of mass $2M$ as show in figure. Initially the block and the man are resting on a rough plank of mass $2M$ as shown in figure. The whole system is resting on a smooth horizontal surface. The man pulls the rope. Pulley is massless and frictionless. What is the magnitude of displacement of the plank when the block meets the pulley ......... $m $ (Man does not leave his position on the plank during the pull).
If pulleys shown in the diagram are smooth and massless and $a_1$ and $a_2$ are acceleration of blocks of mass $4 \,kg$ and $8 \,kg$ respectively, then
A ladder rests against a frictionless vertical wall, with its upper end $6\,m$ above the ground and the lower end $4\,m$ away from the wall. The weight of the ladder is $500 \,N$ and its C. G. at $1/3^{rd}$ distance from the lower end. Wall's reaction will be, (in Newton)
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 .......... $m/s$