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 `(g_1//g_2)` at their surfaces 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))`