A solid sphere rolls down without slipping on an inclined plane, then percentage of rotational kinetic energy of total energy will be ........ $\%.$

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 :

Two coaxial discs, having moments of inertia $I_1$ and $\frac{I_1}{2}$ are a rotating with respectively angular velocities $\omega_1$ and $\frac{\omega_1}{2}$, about their common axes. They are brought in contact with each other and thereafter they rotate with a common angular velocity. If $E_f$ and $E_i$ are the final and initial total energies, then $(E_f -E_i)$ is

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

$A$ 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 sphere of mass $50\,gm$ and diameter $20\,cm$ rolls without slipping with a velocity of $5\,cm/sec$ . Its total kinetic energy is