If the mass of the earth is 100times that of the moon and it's diameter 5 Times that of moon Comparee the weight of a body on the surface of thee moon with its weight on the surface of the earth.
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Weight on earth will be 4 times that of weight on moon.
Explanation :
Let the mass of the moon = m
=> Mass of earth = 100m
Let the radius of moon = r
=> Radius of earth = 5r
We know that acceleration due to gravity is given by,
g = GM/R²
For moon acceleration due to gravity
g₁ = Gm/r²
For earth acceleration due to gravity
g₂ = Gx100m/(5r)² = 4Gm/r²
we know that weight of a body is given by,
weight = mass x acceleration due to gravity
weight on moon ,
w₁ = mass x Gm/r²
similarly weight on earth,
w₂ = mass x 4Gm/r² = 4w₁
Hence weight on earth will be 4 times that of weight on moon.
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