The temperature at which the $r.m.s.$ speed of hydrogen molecules is equal to the escape velocity on the Earth's surface will be ...... $K$.

When the r.m.s. velocity of a gas is denoted by '$v$' at temperature '$T$',which of the following relations is true?

Three particles have speeds of $2u$,$10u$,and $11u$. Which of the following statements is correct?

The $r.m.s.$ speed of the molecules of a gas in a vessel is $400 \; m/s$. If half of the gas leaks out,at constant temperature,the $r.m.s.$ speed of the remaining molecules will be ..... $m/s$.

When the temperature of an ideal gas is increased from $27^\circ C$ to $227^\circ C$,its $r.m.s.$ speed changes from $400 \ m/s$ to $V_s$. The value of $V_s$ is ........ $m/s$.

If the ratio of vapour density for hydrogen and oxygen is $\frac{1}{16}$,then under constant pressure,the ratio of their rms velocities will be