A uniform circular disc of moment of inertia $0.2 \mathrm{kg}.{\mathrm{m}}^2$ and radius $0.15 \mathrm{m}$ is mounted on a horizontal cylindrical axle of radius $0.015 \mathrm{m}$ and negligible mass. Calculate the angular velocity acquired from rest by the application for $12$ seconds of force of $20 \mathrm{N}$ tangential to the axle.

A small sphere rolls down without slipping from the top of a track in a vertical plane. The track has an elevated section and a horizontal part. The horizontal part is $1.0$ metre above the ground level and the top of the track is $2.4$ metre above the ground. Find the distance on the ground with respect to the point $B$ (which is vertically below the end of the track as shown in the figure, where the sphere lands. During its flight as a projectile, does the sphere continue to rotate about its centre of mass? Explain.

A rod of length $L$ and mass $M$ is hinged at a point $O$. A small bullet of mass $m$ hits the rod as shown in Fig. 11.152. The bullet gets embedded in the rod. Find angular velocity of the system just after impact.