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The ratio of the masses and radii of two...

The ratio of the masses and radii of two planets are 2 : 3 and 4 : 9. What is the ratio of the escape speed at their surface ?

Text Solution

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`(V_(1))/(V_(2)) = ? , (M_(1))/(M_(2)) = 2/3 and (R_(1))/(R_(2)) = 4/9 `
As we know ` V = sqrt((2GM)/R)`
` :. (V_(1))/(V_(2)) = sqrt((M_(1))/(M_(2)) xx(R_(2))/(R_(1)))`
` = sqrt(2/3 xx9/4 ) = sqrt(3/2)`
` :. V_(1) :V_(2) = sqrt(3) : sqrt(2)`
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