If the temperature of a gas is increased from $27^{\circ} C$ to $159^{\circ} C$, then the percentage increase in the $rms$ speed of the gas molecules is

The temperature at which the root mean square velocity of hydrogen molecules equals their escape velocity from the Earth is closest to: [Boltzmann constant $k_B = 1.38 \times 10^{-23} \, J/K$,Avogadro number $N_A = 6.02 \times 10^{23} \, mol^{-1}$,Molar mass of $H_2 = 2 \times 10^{-3} \, kg/mol$,Radius of Earth $R_e = 6.4 \times 10^6 \, m$,Gravitational acceleration $g = 10 \, m/s^2$]

Six molecules of a gas in a container have speeds $2 \,m/s, 5 \,m/s, 3 \,m/s, 6 \,m/s, 3 \,m/s$ and $5 \,m/s$. The root mean square (r.m.s.) speed is: (in $\,m/s$)

When the rms velocity of a gas is denoted by $V$,which of the following relations is true? ($T=$ absolute temperature of the gas)

The root mean square velocity of a gas molecule of mass $m$ at a given temperature is proportional to

The respective speeds of the molecules are $1, 2, 3, 4$ and $5 \ km/sec$. The ratio of their $r.m.s.$ velocity and the average velocity will be