Revive! I need a solution. Swaraj or Aditya or anyone. Help!
Q.Find the minimum radius of a planet of density rho temperature T which can retain oxygen in it's atmosphere.The mass of oxygen is M and the acceleration due to gravity is g m/s^2.
Ans:sqrt[(9RT)/8*G*m*rho*pie]
here i get the ans if i do
V( escape)> V(rms) ,
my doubt is
why do i not do
V(esc) > V(avg)

UP 0 DOWN 0 0 6
6 Answers
Average KE at surface=(3/2)RT
PE at surface=Gmρ*4/3πR^{3}/R
Now simply equate energy at surface and infinity.
total KE = 1/2*m*v_{1}^{2} + 1/2*m*v_{2}^{2} + .... + 1/2*m*v_{n}^{2}
= 1/2 * (nm) * (v_{1}^{2} + v_{2}^{2}+......+v_{n}^{2})n
= 1/2* (M)*v_{rms} ^{2}
hence you cannot use v_{avg}
i think because you need the velcity associated with kinetic energy of the gas which is the v(rms)
equate energies at surface and at infinity..:)
that will do the sum! :)