Question

If the mass of the moon is 7.35×10²²kg and the moon's radius is R=1738000. meters so what would be the acceleration of gravity on surface of the moon and also prove that the moon the acceleration of gravity is about 16% that on Earth​

Answer 1

Solution

Given :-

• Mass of moon (M) = 7.35 × 10²² kg
• Radius is 1738000 meters

Find :-

• acceleration of gravity on surface of the moon

Explanation

Using Formula

$\dag\boxed{\underline{\tt{\red{\:g\:=\:\dfrac{GM}{R^2}}}}}$

Here,

• G = Gravitational constant [6.7 × 10^(-11) Nm²/kg² ]
• M =Mass of Moon
• R = Radius of Moon

Now, Keep all above Values,

The acceleration due to gravity on the surface of the moon given by,

==> g = [6.7 × 10^(-11) × 7.35 × 10²²]/[1738 × 10³]²

==> g = (6.7 × 7.35 × 10¹¹)/(1738² × 10⁶)

==> g = (49.345 × 10⁵)/(30,20,644)

==> g = 49,34,500/30,20,644

==> g = 1.63 m/s²

We Know,

• Gravity of earth = 9.8 m/s²

Now, Calculate what percentage gravity of moon comparison to earth gravity .

now,

==> % gravity of moon = 1.63 × 100/9.8

==> % gravity of moon = 1630/98

==> % gravity of moon = 16.6 %

We take if approx values.

then we can say this only 16%.

Hence

• The acceleration due to gravity on the surface of the moon is 1.63 m/s²

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