gravitation question

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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)

#Physics #Mechanics

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6 Answers

1

Anirudh Kumar ·2011-01-11 06:24:18

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

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49

Subhomoy Bakshi ·2011-01-11 13:02:17

equate energies at surface and at infinity..:)

that will do the sum! :)

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Vivek @ Born this Way ·2012-04-05 03:17:30

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

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Swaraj Dalmia ·2012-04-05 03:35:49

Average KE at surface=(3/2)RT
PE at surface=-GmÏ*4/3Ï€R³/R

Now simply equate energy at surface and infinity.

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262

Aditya Bhutra ·2012-04-05 05:57:11

total KE = 1/2*m*v₁² + 1/2*m*v₂² + .... + 1/2*m*v_n²
= 1/2 * (nm) * (v₁² + v₂²+......+v_n²)n
= 1/2* (M)*v_rms ²

hence you cannot use v_avg

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Vivek @ Born this Way ·2012-04-06 01:16:19

Average KE should remain the same at infinity too na?

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