gravitation question

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)

6 Answers

71
Vivek @ Born this Way ·

Revive! I need a solution. Swaraj or Aditya or anyone. Help!

21
Swaraj Dalmia ·

Average KE at surface=(3/2)RT
PE at surface=-Gmρ*4/3πR3/R

Now simply equate energy at surface and infinity.

262
Aditya Bhutra ·

total KE = 1/2*m*v12 + 1/2*m*v22 + .... + 1/2*m*vn2
= 1/2 * (nm) * (v12 + v22+......+vn2)n
= 1/2* (M)*vrms 2

hence you cannot use vavg

71
Vivek @ Born this Way ·

Average KE should remain the same at infinity too na?

1
Anirudh Kumar ·

i think because you need the velcity associated with kinetic energy of the gas which is the v(rms)

51
Subhomoy Bakshi ·

equate energies at surface and at infinity..:)

that will do the sum! :)

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