The planets with radii `R_(1)` and `R_(2)` have densities `p_(1),p_(2)` respectively. Their atmospheric pressues are `p_(1)` and `p_(2)` respectively.Therefore, the ratio of masses of their atmospheres, neglecting variation of g within the limits of atmoshpere is

Options

A. `(p_(1)R_(2)rho_(1))/(p_(2)R_(1)rho_(2))`
B. `(p_(1)R_(2)rho_(2))/(p_(2)R_(1)rho_(1))`
C. `(p_(1)R_(1)rho_(1))/(p_(2)R_(2)rho_(2))`
D. `(p_(1)R_(1)rho_(2))/(p_(2)R_(2)rho_(1))`

Answer

D

Explanation

`p=rho_(atm)gh=m/(4/3pi[(R+h)^(3)-R] (GM)/(R^(2))h`
`implies p=m/(4/3piR^(3)[(1+h/R)^(3)-1)]xx(G4/3piR^(3)l_(0))/(R^(2))xxh`
`m/(4/3piR^(3)[(1+(3h)/h-1]xxG4/3piRl_(0)h` (Here `M=4/3piR^(3)l_(0)`)
Here `p=(mGrho)/(3R)`
`=:. Mprop(pR)/rho`