The height ' $h$ ' above the earth's surface at which the value of acceleration due to gravity $(\mathrm{g})$ becomes $\left(\frac{\mathrm{g}}{3}\right)$ is ( $\mathrm{R}=$ radius of the earth)

In an isobaric process of an ideal gas, the ratio of work done by the system to the heat supplied $\left(\frac{W}{Q}\right)$ is

The threshold frequency of a metal is ' $F_0$ '. When light of frequency $2 F_0$ is incident on the metal plate, the maximum velocity of photoelectron is ' $\mathrm{V}_1$ '. When the frequency of incident radiation is increased to ' $5 \mathrm{~F}_0$ ', the maximum velocity of photoelectrons emitted is ' $V_2$ '. The ratio of $V_1$ to $V_2$ is

A charged particle is moving in a uniform magnetic field in a circular path with radius ' $R$ '. When the energy of the particle is doubled, then the new radius will be