The ratio of acceleration due to gravity on the earth to the moon is : (Take Mass of the earth $= M_{e}$ , the radius of earth $= R_{e}$ , Mass of the moon $= M_{m}$ and the radius of moon $= R_{m}$ )

$\frac{M_{m} {R_{m}}^{2}}{M_{e} {R_{e}}^{2}}$

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$\frac{M_{e} {R_{m}}^{2}}{M_{m} {R_{e}}^{2}}$

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$\frac{M_{e} R_{m}}{M_{m} R_{e}}$

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$\frac{M_{e} {R_{m}}^{3}}{M_{m} {R_{e}}^{3}}$

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Solution

The correct option is B
$\frac{M_{e} {R_{m}}^{2}}{M_{m} {R_{e}}^{2}}$

Given,

Mass of the earth $= M_{e}$ , the radius of earth $= R_{e}$ , Mass of the moon $= M_{m}$ and the radius of moon $= R_{m}$

As we know that acceleration due to gravity on earth $g = G \frac{M_{e}}{{R_{e}}^{2}}$

acceleration due to gravity on moon $g_{m} = G \frac{M_{m}}{{R_{m}}^{2}}$

Therefore, $\frac{g}{g_{m}} = \frac{G \frac{M_{e}}{{R_{e}}^{2}}}{G \frac{M_{m}}{{R_{m}}^{2}}}$ $= \frac{M_{e} {R_{m}}^{2}}{M_{m} {R_{e}}^{2}}$

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Similar questions

Acceleration due to gravity on moon is $\frac{1}{6}$ of the acceleration due to gravity on earth. If the ratio of densities of earth $(ρ_{m})$ and moon $(ρ_{e})$ is $(\frac{ρ_{e}}{ρ_{m}}) = \frac{5}{3}$ then radius of moon $R_{m}$ in terms of $R_{e}$ will be