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

Two bodies rotate with kinetic energies 'E$$_1$$' and 'E$$_2$$'. Moments of inertia about their axis of rotation are 'I$$_1$$' and 'I$$_2$$'. If $$\mathrm{I_1=\frac{I_2}{3}}$$ and E$$_1$$ = 27 E$$_2$$, then the ratio of angular momenta 'L$$_1$$' to 'L$$_2$$' is

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

Three points masses, each of mass $m$ are placed at the corners of an equilateral triangle of side $\ell$. The moment of inertia of the system about an axis passing through one of the vertices and parallel to the side joining other two vertices, will be