Archimedes supposedly was asked to determine whether a crown made for the king consisted of pure gold (density of gold is 19.3 × 103 kg/m3). According to legend, he solved this problem by weighing the crown first in air and then in water. Suppose the scale read 8.90 N when the crown was in air and 7.80 N when it was in water. Find the density. What should Archimedes have told the king?

Explanation:

First, we can find the mass of the object in air

Since W = mg

m = W/g = (8.9)/(9.8) = 0.908 kg

Then, by Archimedes principle, we can find its volume. The volume is found by the weight of the water displaced by the formula

W = Vρg

The Weight is the difference in scale readings. The density of water is 1000 kg/m3

(8.9- 7.8) = V(1000)(9.8)

Thus V = 1 X 10-4 m3

Then, since density is mass / volume

ρ = 0.908/1 X 10-4

ρ = 8254 kg/m3 which is 8 X 103 kg/m3

The density of gold is 19.3 X 103 kg/m3

Since those densities are not the same, the crown is either hollow or not pure gold

the body's situation won't change the forces are equal opposit and on the same body