$A$ disc with a moment of inertia of $\frac{9.8}{\pi^2} \ kg \ m^2$ is rotating at $600 \ rpm$. If the rotational frequency changes from $600 \ rpm$ to $300 \ rpm$,the work done is .......... $J$.

$A$ 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:

The $M.I.$ of a body about the given axis is $1.2 \, kg \cdot m^2$ and initially the body is at rest. In order to produce a rotational kinetic energy of $1500 \, J$,an angular acceleration of $25 \, rad/s^2$ must be applied about that axis for a duration of ........ $s$.

$A$ wheel of moment of inertia $10 \ kg \cdot m^2$ is rotating at $10$ rotations per minute. The work done in increasing its speed to $5$ times its initial value will be .......... $J$.

$A$ thin uniform circular disc of mass $\frac{10}{\pi^2} \,kg$ and radius $2 \,m$ is rotating about an axis passing through its centre and perpendicular to its plane. The work done to increase the angular speed of the disc from $90 \,rev/min$ to $120 \,rev/min$ is (in $\,J$)

$A$ thin uniform rod of length $L$ and mass $M$ is swinging freely about a horizontal axis passing through its end. Its maximum angular speed is $\omega$. Its centre of mass rises to a maximum height of (where $g$ is the acceleration due to gravity):