Question

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

Answer 1

because the gravity of the moon is one by vi of the earth therefore the weight of the object decreases 1 by 6 th on the moon

Answer 2

Weight = (mass) × (acceleration due to gravity of planet)

At surface of earth
Weight = mg

At surface of Moon
Weight = mg / 6
[∵ Acceleration due to Moon’s gravity = (Acceleration due to Earth’s gravity)/6]

∴ Weight on moon = 1/6 × Weight on earth
____________________________

Q.
How acceleration due to moon’s gravity = g/6?

Ans.
Here is mathematical proof:-
Mass of Moon = 7.34 × 10²² kg
Radius of moon = 1737 km = 1.737 × 10⁶ m

a = GM / R²
= (6.67 × 10⁻¹¹ × 7.34 × 10²²) / (1.737 × 10⁶)²
= 1.6 m/s²

We know that acceleration due to Earth’s gravity (g) is 9.8 m/s²

Comparing a and g we get
a = g/6
Hence proved.