The two planets with radii R1,R2 have densities ρ1,ρ2 and atmospheric pressures P1 and P2 respectively. Therefore the ratio of masses of their atmospheres, neglecting variation of g within the limits of atmosphere, is

Question

The two planets with radii R1,R2 have densities ρ1,ρ2 and atmospheric pressures P1 and P2 respectively. Therefore the ratio of masses of their atmospheres, neglecting variation of g within the limits of atmosphere, is (A) (P1R2ρ1/P2R1ρ2) (B) (P1R2ρ2/P2R1ρ1) (C) (P1R1ρ1/P2R2ρ2) (D) (p1R1ρ2/p2R2ρ1)

Tardigrade Admin · Accepted Answer

Acceleration due to gravity, beginarrayl g =( GM / R 2)=(4/3) π ρ GR ∴ ( g 1/ g 2)=(ρ1 R 1/ρ2 R 2) endarray Atmospheric pressure can be given by p =( W / S ) where, W = weight of atmosphere, S = Surface area of the planet ∴ ( m 1/ m 2)=(ρ1 S 1 g 2/ρ2 S 2 g 1)=( p 1 ⋅(4 π R 12)/ p 2(4 π R 22)) ⋅ (ρ2 R 1/ρ1 R 1)=( p 1 R 1 ρ2/ p 2 R 2 ρ1)

Q. The two planets with radii $R_{1}, R_{2}$ have densities $ρ_{1}, ρ_{2}$ and atmospheric pressures $P_{1} an d P_{2}$ respectively. Therefore the ratio of masses of their atmospheres, neglecting variation of $g$ within the limits of atmosphere, is

$\frac{P _{1} R _{2} ρ _{1}}{P _{2} R _{1} ρ _{2}}$

$\frac{P _{1} R _{2} ρ _{2}}{P _{2} R _{1} ρ _{1}}$

$\frac{P _{1} R _{1} ρ _{1}}{P _{2} R _{2} ρ _{2}}$

$\frac{p _{1} R _{1} ρ _{2}}{p _{2} R _{2} ρ _{1}}$

Q. The two planets with radii R1​,R2​ have densities ρ1​,ρ2​ and atmospheric pressures P1​andP2​ respectively. Therefore the ratio of masses of their atmospheres, neglecting variation of g within the limits of atmosphere, is

P2​R1​ρ2​P1​R2​ρ1​​

P2​R1​ρ1​P1​R2​ρ2​​

P2​R2​ρ2​P1​R1​ρ1​​

p2​R2​ρ1​p1​R1​ρ2​​

Q. The two planets with radii $R_{1}, R_{2}$ have densities $ρ_{1}, ρ_{2}$ and atmospheric pressures $P_{1} an d P_{2}$ respectively. Therefore the ratio of masses of their atmospheres, neglecting variation of $g$ within the limits of atmosphere, is

$\frac{P _{1} R _{2} ρ _{1}}{P _{2} R _{1} ρ _{2}}$

$\frac{P _{1} R _{2} ρ _{2}}{P _{2} R _{1} ρ _{1}}$

$\frac{P _{1} R _{1} ρ _{1}}{P _{2} R _{2} ρ _{2}}$

$\frac{p _{1} R _{1} ρ _{2}}{p _{2} R _{2} ρ _{1}}$