Question

Why is the weight of an object on the moon 1/6 th its weight on the earth?

Answer 1

because the mass of moon is almost 1/6th of the mass of earth. So the value of g the acceleration due to gravity and thus the weight W = Mg becomes 1/6th of that of earth.
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Answer 2

Weight an object is 1/6th to that on Earth is because acceleration due to gravity on the moon is about 1/6th to that of Earth.

Acceleration due to gravity on earth = 9.8 M/s²
While,
Acceleration due to gravity on Moon is about 1.63 m/s².

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