Two planets `A` and `B` have the same material density. If the radius of `A` is twice that of `B`, then the ratio of the escape velocity `(v_(A))/(v_(B))` is

Options

A. 2
B. `sqrt(2)`
C. `1//sqrt(2)`
D. `1//2`

Answer

A

Explanation

`V_(e )=sqrt((2GM)/(R )) rArr V_(e )= sqrt((2G.(4)/(3)piR^(3)rho)/(R )) rArr V_(e ) = sqrt(8G pi rho R)`
`(V_(A))/(V_(B))=(R_(A))/(R_(B)) rArr (V_(A))/(V_(B))=(2)/(1)`