In a hydrogen atom in its ground state, the first Bohr orbit has radius $r_1$. The electron's orbital speed becomes one-third when the atom is raised to one of its excited states. The radius of the orbit in that excited state is

' $N$ ' molecules of gas $A$, each having mass ' $m$ ' and ' 2 N ' molecules of gas B , each of mass ' 2 m ' are contained in the same vessel which is at constant temperature ' T '. The mean square velocity of $B$ is $V^2$ and mean square of x -component of A is $\omega^2$. The value of $\frac{\omega^2}{\mathrm{~V}^2}$ is

For a satellite moving in an orbit around the earth at height ' $h$ ' the ratio of kinetic energy to potential energy is

The number of turns in the primary of a transformer are 1000 and in secondary 3000. If 80 V a.c. is applied to the primary, the potential difference per turn of the secondary coil is