The temperature at which r.m.s. velocity of hydrogen molecules is 4.5 times that of an oxygen molecule at $47^{\circ} \mathrm{C}$ is (Molecular weight of hydrogen and oxygen molecules are 2 and 32 respectively)

A sonometer wire is stretched by hanging a metal bob. The fundamental frequency of vibration of wire is ' $n_1$ '. When the bob is completely immersed in water, the frequency of vibration of wire becomes ' $n_2$ '. The relative density of the metal of the bob is

For a body performing simple harmonic motion, its potential energy is $\mathrm{E}_{\mathrm{x}}$ at displacement x and $\mathrm{E}_{\mathrm{y}}$ at displacement y from mean position. The potential energy $E_0$ at displacement $(x+y)$ is

Charge on a parallel plate capacitor of capacity C is Q , the electric field intensity between its two plates separated by a distance of $t$ is