First slide

Gravitational field intensity

Question

The mass of the moon is 1/81 of the earth but the gravitational pull is 1/6 of the earth. It is due to the fact that

Moderate

A

The radius of the moon is 81/6 of the earth
B

The radius of the earth is $9 / \sqrt{6}$ of the moon
C

Moon is the satellite of the earth
D

None of the above

Solution

Gravitational pull depends upon the acceleration due to gravity on that planet.
$\begin{array}{l} ∴ M_{m} = \frac{1}{81} M_{e}, g_{m} = \frac{1}{6} g_{e} \\ g = \frac{Gm}{R^{2}} \Rightarrow \frac{R_{e}}{R_{m}} = {(\frac{M_{e}}{M_{m}} \times \frac{g_{m}}{g_{e}})}^{1 / 2} = {(81 \times \frac{1}{6})}^{1 / 2} \\ R_{e} = \frac{9}{\sqrt{6}} R_{m} \end{array}$

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