The acceleration due to gravity on the surface of the moon is 1.62 ms⁻². The radius of the moon is 1740 km. Find the mass of the moon. Ans. (7.35x10²² kg)
Given:
Value of Gravitational acceleration on the surface of the Moon = gₘ = 1.62 m s⁻²
Radius of the Moon = Rₘ = 1740 Km = 1.740 x 10³x 10³ m = 1.740 x 10⁶ m
Gravitational Constant = G = 6.67 x 10⁻¹¹N m² Kg⁻²
To Find:
Mass of the Moon = Mₘ = ? kg
Solution:
Let m be the mass of the body on the surface of the Moon and Mₘ is the mass of the Moon. The distance between their centres is equal to the radius Rₘ of the Moon and then According to the Law of Gravitation we have
F = GmMₘRₘ2 -----eqn (1)
But according to the 2nd law of Newton
F = W = mgₘ ----eqn (2)
By comparing these two Eqns 1 & 2 we have
mgₘ = GmMₘR2
m will cancel from both sides hence
gₘ = GMₘRₘ2
or
Mₘ = gₘRₘ2G
By putting values
Mₘ = 1.62ms⁻²x(1.740x10⁶m)26.67x10⁻¹¹Nm²Kg⁻²
Mₘ = 1.62ms⁻²x3.0276x10¹²m²6.67x10⁻¹¹Nm²Kg⁻²
Mₘ = 1.62x3.02766.67 x 10¹²⁺¹¹ Kg
Mₘ = 0.735x 10²³ Kg
or
Mₘ = 7.35x 10²² Kg
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