The ratio of accelerations due to gravity g1 - g2 on the surfaces of two planets is 5-2 and the ratio of their respective average densities -1 - -2 is 2-1- What is the ratio of respective escape velocities v1 - v2 from the surface of the plants-

The radii of two planets are respectively $R_{1}$ and $R_{2}$ and their densities are respectively $ρ_{1} a n d ρ_{2}$ . The ratio of the accelerations due to gravity at their surface is

Q. Pertaining to two planets, the ratio of escape velocities from respective surfaces is

1 : 2

, the ratio of the time period of the same simple pendulum at their respective surfaces is

2 : 1

(in same order). Then the ratio of their average densities is

Q. The radii of two planets are respectively

R_{1}

and

R_{2}

and their densities are respectively

ρ_{1}

and

ρ_{2}

. The ratio of the accelerations due to gravity at their surfaces is

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The ratio of accelerations due to gravity g1:g2 on the surfaces of two planets is 5:2 and the ratio of their respective average densities ρ1:ρ2 is 2:1. What is the ratio of respective escape velocities v1:v2 from the surface of the plants?

The correct option is B 5:2√2−GmmR+12mv2=0v=√2GMR=√2GMR2R=√2gRGρ1×43πR31R21Gρ2×43πR32R22=52⇒R1R2=52×ρ2ρ1=52×12=54∴V1V2=√g1R1g2R2=√52×54=52√2

The ratio of accelerations due to gravity $g_{1} : g_{2}$ on the surfaces of two planets is $5 : 2$ and the ratio of their respective average densities $ρ_{1} : ρ_{2}$ is $2 : 1$ . What is the ratio of respective escape velocities $v_{1} : v_{2}$ from the surface of the plants?