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The radius of a planet is double that of...

The radius of a planet is double that of earth but their average are the same. If the escape velocities at the planet and the earth are `v_(p)` and `v_( e)` respectively , then prove that `v_(p) = 2 v_(e)`.

Text Solution

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`v_(e)sqrt((2GM)/R)=sqrt((2G)/Mxx4/3piR^(3)rho)=Rsqrt((8pi)/3GKrho)`
`(v_(p))/(v_(e))=(R_(p))/(R_(e))=(2R_(e))/(R_(e))=2` or `v_(p)=2v_(e)`
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