Question

Archimedes’ principle can be used to calculate the density of a fluid as well as that of a solid. Suppose a chunk of iron with a mass of 375 g in air is found to have an apparent mass of 355 g when completely submerged in an unknown liquid

What mass of fluid, in grams, does the iron displace?

What is the volume, in cubic centimeters, of the iron, given its density is 7.80 g/cm³?

Calculate the fluid’s density, in grams per cubic centimeter.

Answer 1

From the given data

Buoyant force = W_true - W_apparent

weight of the displaced fluid = m_true*g - m_apparent*g

m_fluid_displaced*g = m_true*g - m_apparent*g

m_fluid_displaced = m_true - m_apparent

= 375 - 355

= 20 grams <<<<<<<<<<-------------Answer

Volume of the chunk of Iron, V = mass/density

= 375/7.8

= 48.08 cm^3 <<<<<<<<<<-------------Answer

density of fluid = m_fluid_dispalced/V

= 20/48.08 <<<<<<<<<<-------------Answer

= 0.416 g/cm^3