An insulated box containing a diatomic gas of molar mass $M$ is moving with velocity $v$. The box is suddenly stopped. The resulting change in temperature is :-

$A$ very tall vertical cylinder is filled with a gas of molar mass $M$ under isothermal conditions at temperature $T$. The density and pressure of the gas at the base of the container are $\rho_0$ and $p_0$,respectively. Choose the correct statement$(s)$.

At which temperature will the speed of sound in hydrogen be the same as the speed of sound in oxygen at $100\,^{\circ}C$?

Column-$I$ represents physical quantity and Column-$II$ represents formula. Match them correctly:

Column-$I$	Column-$II$
$(a)$ Kinetic energy per unit mole of gas.	$(i)$ $\frac{1}{2}RT$
$(b)$ Kinetic energy per one molecule of gas.	$(ii)$ $\frac{3}{2}RT$
	$(iii)$ $\frac{3}{2}k_BT$

The same gas is filled in two vessels of the same volume at the same temperature. If the ratio of the number of molecules is $1:4$,then:
$A.$ The $r.m.s.$ velocity of gas molecules in the two vessels will be the same.
$B.$ The ratio of pressure in these vessels will be $1:4$.
$C.$ The ratio of pressure will be $1:1$.
$D.$ The $r.m.s.$ velocity of gas molecules in the two vessels will be in the ratio of $1:4$.

$A$ horizontal uniform glass tube of $100 \ cm$ length, sealed at both ends, contains a $10 \ cm$ mercury column in the middle. The temperature and pressure of air on either side of the mercury column are $31^{\circ} C$ and $76 \ cm$ of mercury, respectively. If the air column at one end is kept at $0^{\circ} C$ and the other end at $273^{\circ} C$, then the pressure of air which is at $0^{\circ} C$ is (in $cm$ of $Hg$):