Two planets of radii (R\_1) and (R\_2) have the same density... | Physics | SolveeIt

Two planets of radii $R_1$ and $R_2$ have the same density. The ratio of the acceleration due to gravity on these planets is

$\frac{R_1}{R_2}$

$\frac{R_2}{R_1}$

$\left(\frac{R_2}{R_1}\right)^2$

$\left(\frac{R_1}{R_2}\right)^2$

Answer

$\frac{R_1}{R_2}$

Explanation

We know acceleration due to gravity of a planet is given by,
$g = \frac{GM}{R^{2}} = \frac{G\rho \frac{4}{3} \pi R^{3}}{R^{2}}$

or, $g = \frac{4}{3}\pi\rho GR$ or , $g \propto R$
$\therefore\:\:\: \frac{g_{1}}{g_{2}} = \frac{R_{1}}{R_{2}}$

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