Question

A body with mass density 0.8g/cm cube and volume 100 cm cube is on the fluid with density 1.2 g/cm cube . Find mass of the body and amount of the volume inside the fluid.

Answer 1

By definition of the density, the mass of the body will be:

$$m = \rho V$$

where $\rho$ is the density and $V$ is the volume of the body. Thus:

$$m = 0.8 g/cm^3\cdot100cm^3 = 80g$$

In equlibrium position forces that are acting on the body are equal. Thus:

$$F_g = F_a$$

where $F_g = mg$ is the force of gravity and $F_a$ is the Archimedes' force.

$$mg = \rho_{lic}gV$$

where $\rho_{lic} =1.2g/cm^3$ is the density of the fluid and $V$ is the volume of the body inside the fluid. Expressing $V$ :

$$V = \dfrac{mg}{\rho_{lic}g} = \dfrac{m}{\rho_{lic}} = \dfrac{80g}{1.2g/cm^3} = 66.7 cm^3$$

Answer. m = 80 g, V = 66.7 cm^3.