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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 surfaces is
[MP PET 1994; Kerala PMT 2008; Similar EAMCET 2000]
(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) \( g_{1}: g_{2}=R_{1} \rho_{2}: R_{2} \rho_{1} \)
(d) \( g_{1}: g_{2}=R_{1} \rho_{1}: R_{2} \rho_{2} \)
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