The moment of inertia of a body about a given axis is $$1.2 \mathrm{~kg} / \mathrm{m}^3$$. Initially the body is at rest. In order to produce rotational kinetic energy of $$1500 \mathrm{~J}$$, an angular acceleration of $$25 \mathrm{rad} / \mathrm{s}^2$$ must be applied about an axis for a time duration of

A disc of radius 0.4 metre and mass 1 kg rotates about an axis passing through its centre and perpendicular to its plane. The angular acceleration is 10 rad s$$^{-2}$$. The tangential force applied to the rim of the disc is

The ratio of radii of gyration of a circular ring and circular disc of the same mass and radius, about an axis passing through their centres and perpendicular to their planes is

A solid sphere of mass $$\mathrm{M}$$, radius $$\mathrm{R}$$ has moment of inertia '$$\mathrm{I}$$' about its diameter. It is recast into a disc of thickness 't' whose moment of inertia about an axis passing through its edge and perpendicular to its plane remains 'I'. Radius of the disc will be