The moon's radius is $\frac{1}{4}$ that of the earth and its mass is $\frac{1}{80}$ times that of the earth. If $g$ represents the acceleration due to gravity on the surface of the earth, that on the surface of the moon is

\frac{g}{4}

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\frac{g}{5}

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\frac{g}{6}

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\frac{g}{8}

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Solution

The correct option is A $\frac{g}{5}$
The gravitational acceleration on surface of a planet is given as:
$g = \frac{G M}{R^{2}}$

Hence $\frac{g_{m}}{g_{e}} = \frac{M_{m}}{M_{e}} . \frac{R_{e}^{2}}{R_{m}^{2}}$ $= \frac{1}{80} . \frac{4^{2}}{1}$ $= \frac{1}{5}$

$⟹ g_{m} = \frac{g}{5}$

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The correct option is A g5The gravitational acceleration on surface of a planet is given as:g=GMR2Hence gmge=MmMe.R2eR2m =180.421 =15⟹gm=g5

The moon's radius is $\frac{1}{4}$ that of the earth and its mass is $\frac{1}{80}$ times that of the earth. If $g$ represents the acceleration due to gravity on the surface of the earth, that on the surface of the moon is

The correct option is A $\frac{g}{5}$
The gravitational acceleration on surface of a planet is given as:
$g = \frac{G M}{R^{2}}$

Hence $\frac{g_{m}}{g_{e}} = \frac{M_{m}}{M_{e}} . \frac{R_{e}^{2}}{R_{m}^{2}}$ $= \frac{1}{80} . \frac{4^{2}}{1}$ $= \frac{1}{5}$

$⟹ g_{m} = \frac{g}{5}$