Question

When a crown of mass 14.7 kg is submerged in water, an accurate scale reads only 13.4 kg. What material is the crown made of?

Answer 1

ρ = 1.13 10⁴ km/m³

Step-by-step explanation:

For this exercise we use Newton's equilibrium equation

B –W + W_scale = 0

Where B is the thrust and W_scale is the balance reading

The push is given by Archimedes' law

B = ρ_water g V

B = W- W_scale

B = m g - m_scale g

Let's calculate

B = 14.7 9.8 - 13.4 9.8

B = 12.74 N

ρ_water g V = 12.74

V = 12.74 / ρ_water g

V = 12.74 / 1000 9.8

V = 0.0013 m³

Let's use density

ρ = m / V

We replace

ρ = 14.7 / 0.0013

ρ = 1.13 10⁴ km/m³