The spherical planets have the same mass but densities in the ratio `1: 8`. For these planets the :

Options

A. acceleration due to gravity will be in the ratio `4:1`
B. acceleration due to gravity will be in the ratio `1:4`
C. escape velocities from their surfaces will be in the ratio `sqrt(2):1`
D. escape velocities from their surfaces will be in the ratio `1:sqrt(2)`

Answer

B, D

Explanation

let both planet have densities e and 8e
`4/3pir_(1)^(3)e=4/3pi_(2)^(3)8e`
`r_(1)=2r_(2)`
`(g_(1))/(g_(2)) =((r_(2))/r_(1))^(2)=1/4`