A coil of radius '$$r$$' is placed on another coil (whose radius is $$\mathrm{R}$$ and current flowing through it is changing) so that their centres coincide $$(\mathrm{R} \gg \mathrm{r})$$. If both the coils are coplanar then the mutual inductance between them is ( $$\mu_0=$$ permeability of free space)

Two capillary tubes of the same diameter are kept vertically in two different liquids whose densities are in the ratio $$4: 3$$. The rise of liquid in two capillaries is '$$h_1$$' and '$$h_2$$' respectively. If the surface tensions of liquids are in the ratio $$6: 5$$, the ratio of heights $$\left(\frac{h_1}{h_2}\right)$$ is

(Assume that their angles of contact are same)

Two spherical black bodies of radii '$$r_1$$' and '$$r_2$$' at temperature '$$\mathrm{T}_1$$' and '$$\mathrm{T}_2$$' respectively radiate power in the ratio $$1: 2$$ Then $$r_1: r_2$$ is

For a particle executing S.H.M., its potential energy is 8 times its kinetic energy at certain displacement '$$x$$' from the mean position. If '$$A$$' is the amplitude of S.H.M the value of '$$x$$' is