Question

The atmosphere on a planet is possible only if [where $v_{rms}$ is root mean square speed of gas molecules on planet and $v_e$ is escape velocity on its surface]

• A. $v_{rms}=v_e$
  
• B. $v_{rms}>v_e$
  
• C. $v_{rms}\le v_e$
  
• D. $v_{rms}<v_e$
  

Answer 1

The correct option is D $v_{rms}<v_e$


If $v_{rms}\ge v_e$ then the gas molecules will escape from the surroundings of the planet, i.e., the gas molecules will be free from gravitational pull of the planet.

So, the atmosphere on a planet is possible, only if $v_{rms}<v_e$

Hence, option (d) is the correct answer.