The speeds of $5$ molecules of a gas (in arbitrary units) are as follows: $2, 3, 4, 5, 6$. The root mean square speed for these molecules is

The rms speed of an oxygen molecule in a vessel at a particular temperature is $\left(1+\frac{5}{x}\right)^{\frac{1}{2}} v$,where $v$ is the average speed of the molecule. The value of $x$ will be: (Take $\pi=\frac{22}{7}$)

The $rms$ speed of gas molecules in a container is $400 \, ms^{-1}$. If half of the gas is removed at a constant temperature,the new $rms$ speed will be .... $ms^{-1}$.

When the temperature of a gas is increased to $3$ times,what will be the change in $v_{rms}$?

When the temperature of an ideal gas is increased from $27^{\circ} C$ to $127^{\circ} C$,calculate the percentage increase in its $v_{\text{rms}}$. (in $\%$)

An ideal gas of molar mass $M_0$ has r.m.s. velocity $V$ at temperature $T$. Then