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

Answer

B

Explanation

`(V_(e1))/(V_(e2))=sqrt((M_(1)R_(2))/(M_(2)R_(1)))=sqrt((R_(1)^(3))/(R_(2)^(3))xx(R_(2))/(R_(1)))=(R_(1))/(R_(2))=(2)/(1)`