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there are two planets.the ratio of radius of the two planets is k but ratio of acceleration due to gravity of both the planets is g.What will be the ratio of their escape velocity?

there are two planets.the ratio of radius of the two planets is k but ratio of acceleration due to gravity of both the planets is g.What will be the ratio of their escape velocity? 

Grade:12

2 Answers

vikas askiitian expert
509 Points
10 years ago

let one planet be a & other b then

Ra/Rb = K    ........1  (given)

g(acc due to gravity)= GM/R2

ga/gb = (Ma/Mb)*(Rb/Ra)2 = 1         (given)

Ma/Mb = (Ra/Rb)2 = K2       ..............2              (from eq 1)

now escape velocity = (GM/R)1/2

 Va/Vb = [(Ma/Mb)(Rb/Ra)]1/2

         =[ k2(1/k)]1/2                    (from eq 1 & 2)

         =k1/2

thus the ratio of escape velocity is K1/2

vikas askiitian expert
509 Points
10 years ago

 approve my ans if u like

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