In case of rotational dynamics, which one of the following statements is correct?

[$\vec{\omega}=$ angular velocity, $\overrightarrow{\mathrm{v}}=$ linear velocity

$\overrightarrow{\mathbf{r}}=$ radius vector, $\vec{\alpha}=$ angular acceleration

$\overrightarrow{\mathrm{a}}=$ linear acceleration, $\overrightarrow{\mathrm{L}}=$ angular momentum

$\overrightarrow{\mathrm{p}}=$ linear momentum, $\bar{\tau}=$ torque,

$\overrightarrow{\mathrm{f}}=$ centripetal force]

A convex lens of focal length ' $f$ ' $m$ forms a real, inverted image twice in size of the object. The object distance from the lens in metre is

The ratio of the wavelength of a photon of energy ' $E$ ' to that of the electron of same energy is ( $\mathrm{m}=$ mass of an electron, $\mathrm{c}=$ speed of light, $\mathrm{h}=$ Planck's constant)

The r.m.s. velocity of hydrogen at S.T.P. is ' $u$ ' $\mathrm{m} / \mathrm{s}$. If the gas is heated at constant pressure till its volume becomes three times, then the final temperature of the gas and the r.m.s. speed are respectively