Rate of flow of heat through a cylindrical rod is ' $\mathrm{H}_1$ '. The temperature at the ends of the rod are ' $T_1$ ' and ' $T_2$ '. If all the dimensions of the rod become double and the temperature difference remains the same, the rate of flow of heat becomes ' $\mathrm{H}_2$ '. Then

A ball rises to surface at a constant velocity in liquid whose density is 4 times greater than that of the material of the ball. The ratio of the force of friction acting on the rising ball and its weight is

An air cored coil has self inductance of 0.1 H . A soft iron core of relative permeability 1000 is introduced and the number of turns is reduced to $\left(\frac{1}{10}\right)^{\text {th }}$. The value of self inductance is now

$\mathrm{L}=2 \mathrm{H}, \mathrm{C}=5 \mathrm{mF}$ and $\mathrm{R}=12 \Omega$ are connected in series to an a.c. generator of frequency 50 Hz . Then