A solid circular disc of mass $50 \mathrm{~kg}$ rolls along a horizontal floor so that its center of mass has a speed of $0.4 \mathrm{~m} / \mathrm{s}$. The absolute value of work done on the disc to stop it is____ $\mathrm{J}$.

An automobile engine develops $100\ kW$ when rotating at a speed of $1800\ rev/min$.  What torque does it deliver .......... $N-m$

$A$ rod is hinged at its centre and rotated by applying a constant torque starting from rest. The power developed by the external torque as a function of time is :

A hollow spherical ball of uniform density rolls up a curved surface with an initial velocity $3\, m / s$ (as shown in figure). Maximum height with respect to the initial position covered by it will be $...........cm$.

This question has Statement $1$ and Statement $2$. Of the four choices given after the Statements, choose the one that best describes the two Statements.
Statement $1$ : When moment of inertia $I$ of a body rotating about an axis with angular speed $\omega $ increases, its angular momentum $L$ is unchanged but the kinetic energy $K$ increases if there is no torque applied on it.
Statement $2$ : $L = I\omega $, kinetic energy of rotation $ = \frac{1}{2}\,I\omega ^2$

If a body completes one revolution in $\pi $ $sec$ then the moment of inertia would be