Question

prove that the weight of object on moon is 1.6 of the weight on the earth

Answer 1

Hello..

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

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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....