If the $u_{rms}$ value of a gas at $27\,^oC$ is $30\,R^{1/2}$,then the molar mass of the gas is ........... $kg/mol$.

At $600 \ K$,the root mean square (rms) speed of gas $X$ (molar mass $= 40 \ g \ mol^{-1}$) is equal to the most probable speed of gas $Y$ at $90 \ K$. The molar mass of the gas $Y$ is $....... \ g \ mol^{-1}$. (Nearest integer)

The $r.m.s.$ velocity of a certain gas is $v$ at $300 \ K$. The temperature,at which the $r.m.s.$ velocity becomes double,is ............... $K$.

The $rms$ velocity of molecules of a gas of density $4 \ kg \ m^{-3}$ and pressure $1.2 \times 10^{5} \ Nm^{-2}$ is (in $ms^{-1}$)

The speeds of four particles are $2, 3, 4,$ and $5 \, cm/s$ respectively. What will be their $rms$ speed?

Which of the following is the correct relationship for the root mean square velocity $(V_{rms})$?