$A$ light rod carries three equal masses $A$,$B$,and $C$ as shown in the figure. If the rod is released from the horizontal position,what will be the velocity of mass $B$ when the rod reaches the vertical position?

$A$ solid sphere of mass $M$ rolls without slipping with velocity $v$ and presses a spring of spring constant $k$ as shown in the figure. The maximum compression in the spring will be:

$A$ disc of mass $1\,kg$ and radius $R$ is free to rotate about a horizontal axis passing through its centre and perpendicular to the plane of the disc. $A$ body of the same mass as that of the disc is fixed at the highest point of the disc. Now the system is released. When the body comes to the lowest position,its angular speed will be $4 \sqrt{\frac{x}{3 R}} \text{ rad s}^{-1}$ where $x=$ (Given $g = 10 \text{ m s}^{-2}$)

$A$ uniform solid cylinder of mass $M$ and radius $R$ can freely rotate around its axis $O$. There is an elastic string of relaxed length $L$ and stiffness $K$ attached to the cylinder and a static wall. Initially,the string is relaxed. As the cylinder starts rotating,the string will wind around the cylinder. The surface of the cylinder is very rough,so the string does not slip on the cylinder's surface. The minimum initial angular speed of the cylinder,${\omega _0}$,so that it can rotate through an angle $2\pi$ is (Assume Hooke's law to be valid.)

$A$ flywheel has a moment of inertia of $4 \ kg \cdot m^2$ and a kinetic energy of $200 \ J$. Calculate the number of revolutions it makes before coming to rest if a constant opposing couple of $5 \ N \cdot m$ is applied to the flywheel.

Match the linear motion formulas in Column-$I$ with their corresponding rotational motion formulas in Column-$II$.

Column-$I$	Column-$II$
$(1)$ $W = F \Delta x$	$(a)$ $P = \tau \omega$
$(2)$ $P = Fv$	$(b)$ $W = \tau \Delta \theta$
	$(c)$ $L = I \omega$