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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?

6 years ago

510 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

6 years ago
510 Points

approve my ans if u like

6 years ago
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