The radii of two planets are respectively `R_(1) and R_(2)` and their densities are respectively `rho_(1) and rho_(2)`.The ratio of the accelerations due to gravity at their surface is

Options

A. `r_(1)rho_(1):r_(2)rho_(2)`
B. `r_(1)rho_(1)^(2):rho_(2)rho_(2)^(2)`
C. `r_(1)^(2)rho_(1):r_(2)^(2)rho_(2)`
D. `r_(1)rho_(2):r_(2)rho_(1)`

Answer

A

Explanation

`g=(GM)/(r^(2))=G4/3(r^(3)rho)/(r^(2))=G4/2pir rho`
`(g_(1))/(g_(2))=(r_(1)rho_(1))/(r_(2)rho_(2))`