The radii of two planets are $R_1$ and $R_2$ and their densities are ${\rho }_1$ and ${\rho }_2$ respectively. If $g_1$ and $g_2$ represent the acceleration due to gravity at their respective surfaces, then $\frac{g_1}{g_2}$ is

• A

  $\frac{{\rho }_1{R}_2^2}{{\rho }_2{R}_1^2}$
• B

  $\frac{{\rho }_1{R}_1^2}{{\rho }_2{R}_2^2}$
• C

  $\frac{{\rho }_2{R}_1}{{\rho }_1{R}_2}$
• Correct answer
  D

  $\frac{{\rho }_1{R}_1}{{\rho }_2{R}_2}$

Hence, the correct answer is option: 'D'.