A planet with radius R and acceleration due to gravity g, will have atmosphere only if r.m.s. speed of air molecules is less than

Question

A planet with radius R and acceleration due to gravity g, will have atmosphere only if r.m.s. speed of air molecules is less than (A) 1.414 √g R (B) 1.732 √g R (C) 2 √g R (D) 3.14 √g R

Tardigrade Admin · Accepted Answer

Minimum speed of air molecules, so that they could escape the planet is given as ve =√2 g R =1.414 √g R So, the planet will have atmosphere only, if rms speed of molecules of air is 1.414 √g R.

Q. A planet with radius $R$ and acceleration due to gravity $g$ , will have atmosphere only if r.m.s. speed of air molecules is less than

$1.414 g R$

$1.732 g R$

$2 g R$

$3.14 g R$

$2.75 g R$

Minimum speed of air molecules, so that they could escape the planet is given as
$v_{e} = 2 g R$
$= 1.414 g R$
So, the planet will have atmosphere only, if rms speed of molecules of air is $1.414 g R$ .

Q. A planet with radius R and acceleration due to gravity g, will have atmosphere only if r.m.s. speed of air molecules is less than

1.414gR​

1.732gR​

2gR​

3.14gR​

2.75gR​

Minimum speed of air molecules, so that they could escape the planet is given as ve​=2gR​ =1.414gR​ So, the planet will have atmosphere only, if rms speed of molecules of air is 1.414gR​.