Two coils have a mutual inductance $5 \times 10^{-3} \mathrm{H}$. The current changes in the first coil according to the equation $I_1=I_0 \sin \omega t$ where $I_0=10 \mathrm{~A}$ and $\omega=100 \pi \mathrm{rad} / \mathrm{s}$. What is the value of the maximum e.m.f. in the coil?

When an air bubble rises from the bottom of lake to the surface, its radius is doubled. The atmospheric pressure is equal to that of a column of water of height ' $H$ '. The depth of the lake is

The period of a planet around the sun is 8 times that of earth. The ratio of radius of planet's orbit to the radius of the earth's orbit is

The magnetic induction due to an ideal solenoid is independent of