Two rods, one of aluminium and the other of steel, having initial lengths ' $\mathrm{L}_1$ ' and ' $\mathrm{L}_2$ ' are connected together to form a single rod of length $\left(L_1+L_2\right)$. The coefficients of linear expansion of aluminium and steel are ' $\alpha_1$ ' and ' $\alpha_2$ ' respectively. If the length of each rod increases by the same amount, when their temperatures are raised by $\mathrm{t}^{\mathrm{L}} \mathrm{C}$, then the ratio $\frac{L_1}{L_1+L_2}$ will be

In an a. c. generator, when the plane of the coil is perpendicular to the magnetic field

Two circular metal plates each of radius ' $r$ ' are kept parallel to each other distance ' $d$ ' apart. The capacitance of the capacitor formed is ' $\mathrm{C}_1$ '. If the radius of each of the plates is increased to $\sqrt{2}$ times the earlier radius and their distance of separation decreased to half the initial value, the capacitance now becomes ' $\mathrm{C}_2$ '. The ratio of the capacitances $\mathrm{C}_1: \mathrm{C}_2$ is

Ratio of radius of gyration of a circular disc to that of circular ring each of same mass and radius around their respective axes is