InterviewSolution
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InterviewSolution
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The escape velocity of a satellite from the surface of a planet is `sqrt(2)` times the orbital velocity of the satellite. If the ratio of the masses of two given planets is 1 : 4 and that of their radii is 1 : 2, respectively, then find the ratio of escape velocities of a satellite from the surfaces of two planets. |
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Answer» (i) `V_(e) = sqrt(2) xx V_(o)` `F = (GMm)/(R^(2)) = (mv_(o)^(2))/(R)` `v_(o) = sqrt((GM)/(R))` `rArr (v_(e1))/(v_(e2)) = (sqrt(2)v_(o1))/(sqrt(2)v_(o1))=sqrt((M_(1))/(R_(1)) xx (R_(2))/(M_(2)))` Given that, `rArr (M_(1))/(M_(2)) = (1)/(4) "and" (R_(1))/(R_(2)) = (1)/(2)` Substitute the value of `M_(1), M_(2), R_(1) "and" R_(2)` and find the ratio of `(V_(e1))/(V_(e2))` `1 : sqrt(2)` |
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