Question

If the mass of the earth is 100 times that of the moon and its diameter 5 times that of moon, compare the weight of a body on the surface of the moon with its weight on the surface of the earth.

Answer 1

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.