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Three planets of same density have radii...

Three planets of same density have radii `R_(1),R_(2)` and `R_(3)` such that `R_(1) = 2R_(2) = 3R_(3)`. The gravitational field at their respective surfaces are `g_(1), g_(2)` and `g_(3)` and escape velocities from their surfaces are `upsilon_(1),upsilon_(2)` and `upsilon_(3)`, then

Text Solution

Verified by Experts

`g=(GM)/(R^(2))=(F((4)/(3)piR^(2)rho))/(R^(2))`
`:.g prop R`
`:.(g_(1))/(g_(2))=(R_(1))/(R_(2))=2`
`v=sqrt(2gR) alpha sqrt(R(R ))` or `V prop R`
`(v_(1))/(v_(2))=(R_(1))/(R_(2))=2`
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