Question

A sample of unknown material weighs 450N in air and 300N when submerged in water with a density of 1000kg/m³.What is the density of the material?

Answer 1

Given:

$mg=450\;\rm N$

$mg-F_b=300\:\rm N$

$\rho_w=1000\:\rm kg/m^3$

The buoyant force

$$F_b=g\rho_wV=150\;\rm N$$

The volume of a body

$$V=m/\rho=450\:{\rm N}/(g\rho)$$

Finally

$$\rho_w/\rho=150/450$$

$$\rho=\rho_w/3=1000/3=333\:\rm kg/m^3$$