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>> $The radius of the Moon is about one - fo$

Question

The radius of the Moon is about one-fourth that of the Earth and acceleration due to gravity on the Moon is about one-sixth that on the Earth. From this we can conclude that the ratio of the mass of Earth in the mass of the Moon is about___________.

A

10

B

100

C

1, 000

D

10, 000

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Solution

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Correct option is B)

g = $\frac{G M _{p l a n e t}}{r ^{2}}$
or $M_{p l a n e t} α g r^{2}$
or mass of moon is = (mass of earth) $\times$ $\frac{1}{6}$ $\times$ $\frac{1}{1 6}$ = $\frac{m a s s o f e a r t h}{9 6}$
so, ans is B

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