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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?
2 Answers
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
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