The ratio of escape velocity at earth `(v_(e))` to the escape velocity at a planet `(v_(y))` whose radius and density are twice

Options

A. `1 : sqrt2`
B. `1: 2`
C. `1 : 2 sqrt2`
D. `1 : 4`

Explanation

`(v_(e))/(v_(p)) = sqrt((2G M_(e) //R_(e))/(2G M_(p) // R_(P))) = sqrt((M_(e))/(M_(p)) (R_(p))/(R_(e)))`
`(M_(e))/(M_(p)) = (rho . (4)/(3) xx R_(e)^(3))/(2 rho . (4)/(3) pi R_(p)^(3)) = (1)/(2) ((1)/(2))^(3) = (1)/(16)`
`= sqrt((1)/(16).2) = sqrt((1)/(8)) = (1)/(sqrt2)`