Consider two spherical planets of same average density. Planet 2 is 8 times as massive as planet 1. The ratio of the acceleration due to gravity of the second planet to that of the first is

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Consider two spherical planets of same average density. Planet 2 is 8 times as massive as planet 1. The ratio of the acceleration due to gravity of the second planet to that of the first is

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answer is B.

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Detailed Solution

$\begin{array}{l} m_{2} = 8 m_{1} \\ \frac{4}{3} {πr}_{2}^{3} d = 8 (\frac{4}{3} {πr}_{1}^{3} d) \\ {(\frac{r_{2}}{r_{1}})}^{3} = 8 \\ \frac{r_{2}}{r_{1}} = (8)^{3} = 2 \\ \frac{g_{1}}{g_{2}} = \frac{m_{1}}{m_{2}} \times \frac{r_{2}^{2}}{r_{1}^{2}} = \frac{1}{8} \times (2)^{2} \\ \frac{g_{1}}{g_{2}} = \frac{1}{2} \\ g_{2} = 2 g_{1} \end{array}$