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

The depth 'd' below the surface of the earth where the value of acceleration due to gravity becomes $$\left(\frac{1}{n}\right)$$ times the value at the surface of the earth is $$(R=$$ radius of the earth)

Silicon and copper are cooled from 300 K to 100 K, the specific resistance (resistivity)

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