Question

A bottle full of meecury has a mass of 720gms.When full of water its mass is 90gms. Calculate the volume of empty density bottle.

Answer 1

The mass of the bottle full of mercury and water:

$$M_1=m+\rho_1V,\\ M_2=m+\rho_2V.$$

Subtract one from another:

$$M_1-M_2=V(\rho_1-\rho_2),\\\space\\ V=\frac{M_1-M_2}{\rho_1-\rho_2}=5·10^{-5}\text{ m}^3,$$

or 0.05 L.

Mass of the bottle:

$$m=M_1-\rho_1V=0.04\text{ kg}.$$

Density of the bottle:

$$\rho=\frac{m}{V}=800\text{ kg/m}^3.$$