The acceleration due to gravity on the moon is only one sixth that of earth. If the earth and moon are assumed to have the same density, the ratio of radii of moon and earth will be

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Solution

The correct option is A

$\frac{1}{6} = \frac{g_{m}}{g_{e}} = \frac{R_{e}^{2} M_{m}}{R_{m}^{2} M_{e}} = \frac{R_{e}^{2} R_{m}^{3}}{R_{m}^{2} R_{e}^{3}} = \frac{R_{m}}{R_{e}}$

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The acceleration due to gravity on the moon is only one sixth that of earth. If the earth and moon are assumed to have the same density, the ratio of radii of moon and earth will be

The correct option is A 16=gmge=R2eMmR2mMe=R2eR3mR2mR3e=RmRe

The correct option is A

$\frac{1}{6} = \frac{g_{m}}{g_{e}} = \frac{R_{e}^{2} M_{m}}{R_{m}^{2} M_{e}} = \frac{R_{e}^{2} R_{m}^{3}}{R_{m}^{2} R_{e}^{3}} = \frac{R_{m}}{R_{e}}$