The moment of inertia of a thin uniform rod of mass 'M' and length 'L' about an axis passing through a point at a distance $$\frac{L}{4}$$ from one of its ends and perpendicular to the length of the rod is

A current $$I=10 \sin (100 \pi t)$$ ampere, is passed in a coil which induces a maximum emf $$5 \pi$$ volt in neighbouring coil. The mutual inductance of two coils is

The average density of the earth is [g is acceleration due to gravity]

Two bar magnets '$$\mathrm{P}$$' and '$$\mathrm{Q}$$' are kept in uniform magnetic field '$$\mathrm{B}$$' with magnetic moments '$$\mathrm{M_P}$$' and '$$\mathrm{M_Q}$$' respectively. Magnet 'P' is oscillating with frequency twice that of magnet 'Q'. If the moment of inertia of the magnet 'P' is twice that of magnet 'Q' then