question_answer

The radii of two planets are respectively \[{{R}_{1}}\] and \[{{R}_{2}}\] their densities are respectively\[{{\rho }_{1}} and {{\rho }_{2}}\]. The ratio of the accelerations due to gravity at their surfaces is       

A) \[{{g}_{1}}:{{g}_{2}}=\frac{{{\rho }_{1}}}{{{R}_{1}}^{2}}:\frac{{{\rho }_{2}}}{{{R}_{2}}^{2}}\]

B) \[{{g}_{1}}:{{g}_{2}}={{R}_{1}}{{R}_{2}}:{{\rho }_{1}}{{\rho }_{2}}\]

C) \[{{g}_{1}}:{{g}_{2}}={{R}_{1}}{{R}_{2}}:{{R}_{2}}{{\rho }_{1}}\]

D) \[{{g}_{1}}:{{g}_{2}}={{R}_{1}}{{\rho }_{1}}:{{R}_{2}}{{\rho }_{2}}\]