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

Heat engine operating between temperature $T_1$ and $T_2$ has efficiency $\frac{1}{6}$. When $T_2$ is lowered by 62 K , its efficiency increases to $\frac{1}{3}$. Then $T_1$ and $T_2$ respectively are

The angle of minimum deviation produced by a thin prism in air is $\delta_1$. If it is immersed in water the angle of minimum deviation is

$$\left[\mathrm{a}_{\mathrm{g}}=\frac{3}{2}, \mathrm{a}_{\mathrm{w}}=\frac{4}{3}\right]$$

An electron is revolving in a circular orbit of radius $r$ in a hydrogen atom. The angular momentum of the electron is L . The relation between dipole moment (m) associated with it, gyromagnetic ratio ( R ) and L is