Question

what would be the mass of the earth if the radius of the earth is reduced to 3÷4

Answer 1

Answer:

Step-by-step explanation:

Two concepts are essential to solve this question

1. Density = Mass/Volume

2. Volume of a sphere is $\frac{4}{3}$ π r³

Let's assume the initial mass of earth was 'm', initial volume was 'v₁' and the initial radius was r.

Since radius is reduced to 3/4,

New volume of Earth (v₂) =  $\frac{4}{3}$ π $\frac{3}{4}$ r³

                                          = $\frac{3}{4}$ * v₁

∴ New Mass of Earth (m₂) = Density * v₂

∵ Density is constant, we will assume that initial and final densities are 'd'

m₂ = d * $\frac{3}{4}$ * v₁

m₂ = dv₁ * $\frac{3}{4}$

m₂ = m₁ * $\frac{3}{4}$

Hope this helps!