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Grade: 12

                        

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? 

10 years ago

Answers : (2)

vikas askiitian expert
509 Points
							

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

10 years ago
vikas askiitian expert
509 Points
							

 approve my ans if u like

10 years ago
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