A planet has twice the radius but the mean density is `1/4` th as compared to earth. What is the ratio of escape velocity from earth to that from the planet

Options

A. `1:1`
B. `1:2`
C. `2:1`
D. `3:1`

Answer

A

Explanation

`v_(e )=sqrt((2GM)/(R ))=sqrt((2G4pi R^(3)d)/(3))=2sqrt(2)R sqrt((G pi d)/(3))`
`therefore (v_(e))/(v_(p))=(2sqrt(2)R sqrt((G pi d)/(3)))/(2sqrt(2)2R sqrt((G pi)/(3)(d)/(4)))=1`