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Two planets of radii $r_{1} a n d r_{2}$ are made from the same material having same density. The ratio of acceleration due to gravity $g_{1} {/g}_{2}$ at the surfaces of the planets is

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{(r_{2} {/r}_{1})}^{2}

r_{1} {/r}_{2}

{(r_{1} {/r}_{2})}^{2}

r_{2} {/r}_{1}

answer is A.

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Detailed Solution

We know,

$g = \frac{G M}{R^{2}}$

$M = ρ X V$ , where $ρ$ is the density and $V$ is the volume.

$g = \frac{G \frac{4}{3} {πR}^{3} ρ}{R^{2}}$

$∴ g = \frac{4}{3} π G ρ R$

$∴ \frac{g_{1}}{g_{2}} = \frac{\frac{4}{3} π G ρ r_{1}}{\frac{4}{3} π G ρ r_{2}} = \frac{r_{1}}{r_{2}}$

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