question_answer

The radii of two planets are R and \[2R\] respectively and their densities  \[\rho \] and \[\rho /2\]respectively. What is the ratio of acceleration due to gravity at their surfaces?                          

Answer:

                Here,                 \[g=\frac{GM}{{{R}^{2}}}=\frac{G}{{{R}^{2}}}.\frac{4}{3}\pi {{R}^{3}}\rho =\frac{4}{3}\pi GR\rho \]                 or            \[g\propto R\rho \]                 \[\therefore \]  \[\frac{{{g}_{1}}}{{{g}_{2}}}=\frac{R\rho }{2R.\frac{\rho }{2}}=\mathbf{1:1}\mathbf{.}\]