$A$ constant power is supplied to a rotating disc. The angular velocity $(\omega)$ of the disc varies with the number of rotations $(n)$ made by the disc as:

To maintain a rotor at a uniform angular speed of $200 \; rad \; s^{-1}$,an engine needs to transmit a torque of $180 \; N \; m$. What is the power required by the engine (in $; kW$)? (Note: uniform angular velocity in the absence of friction implies zero torque. In practice,applied torque is needed to counter frictional torque). Assume that the engine is $100 \%$ efficient.

$A$ thin meter rod is placed with one end on the ground. It is allowed to fall such that the contact point remains fixed. Find the velocity of the upper end when it hits the ground.

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

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

$A$ tangential force $F$ is applied on a disc of radius $R$,due to which it deflects through an angle $\theta$ from its initial position. The work done by this force would be

$A$ rod of length $1 \ m$ is held vertically and allowed to fall such that its lower end remains fixed on the ground. The velocity of the other end of the rod when it hits the ground is ......... $m/s$ $(g = 9.8 \ m/s^2)$.