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. `g_(1):g_(2)=(rho_(1))/(R_(1)^(2)):(rho_(2))/(R_(2)^(2))`
B. `g_(1):g_(2)=R_(1)R_(2):rho_(1)rho_(2)`
C. `g_(1):g_(2)=R_(1)rho_(2)^(2):R_(2)rho_(1)`
D. `g_(1):g_(2)=R_(1)rho_(1)^(2):R_(2)rho_(2)`

Answer

D

Explanation

Acceleration due gravity `g=4/3pi rho GR`
`:. g_(1):g_(2)=R_(1)rho_(1):R_(2)rho_(2)`