Question

Suppose a cube of osmium with a mass of 36.52 kg is submerged in rubbing alcohol. The buoyant force over the cube is 1.25 x 10 to the power of 1. Given that rubbing alcohol has the density of 7.86 x 10 to the power of 2 kg/m3. What is the gravitational force of the cube of osmium? What is the density of the osmium in scientific notation?

Answer 1

The gravitational force of the cube of osmium is the consequence of presence of gravitation:

$$F_g=mg=36.52\cdot9.8=358\text{ N}.$$

To find the density of the osmium by dividing its mass by volume, write the equation for the buoyant force:

$$F_b=\rho_\text{alc} gV_\text{osm},\\ \space\\ V_\text{osm}=\frac{F_b}{\rho_\text{alc} g},$$

now it's time to find the density:

$$\rho_\text{osm}=\frac{m}{V_\text{osm}}=\frac{\rho_\text{alc} gm}{F_b},\\ \space\\ \rho_\text{osm}=\frac{786\cdot9.8\cdot36.52}{12.5}=22505\text{ kg/m}^3.$$

The density of the osmium in scientific notation

$$\rho_\text{osm}=22.5\cdot10^3\text{ kg/m}^3.$$