Moment of inertia of a body about a given axis is $1.5\, kg\, m^2$ Initially the body is at rest. In order to produce a rotational kinetic energy of $1200\, J$, the angular acceleration of $20\, rad/s^2$ must be applied about the axis of rotation for a duration of ......... $\sec$.

A wheel is rotaing freely with an angular speed $\omega$ on a shaft. The moment of inertia of the wheel is $I$ and the moment of inertia of the shaft is negligible. Another wheel of momet of inertia $3I$ initially at rest is suddenly coupled to the same shaft. The resultant fractional loss in the kinetic energy of the system is :

If the rotational kinetic energy of a body is increased by $300\ \%$ then the percentage increase in its angular momentum will be .......... $\%$

A solid sphere rolls without slipping and presses a spring of spring constant $k$ as shown in figure. Then, the maximum compression in the spring will be

For a rolling spherical shell, the ratio of rotational kinetic energy and total kinetic energy is $\frac{x}{5}$. The value of $x$ is ................

A small object of uniform density rolls up a curved surface with an initial velocity $v$. It reaches up to a maximum height of $\frac{3 \mathrm{v}^2}{4 \mathrm{~g}}$ with respect to the initial position. The object is