Worked Examples-Calculation Part 2 - Measurement

Considered Formula;

$$\text {i)}\quad W = mg$$ $$\qquad \text {Where}~~W \to Weight,\quad m \to Mass \\\qquad g \to Acceleration~due~to~gravity$$ $$\text {ii)}\quad \rho = \frac {m_1 - m_0}{V}$$ $$\qquad \text {Where}~~\rho \to Density,\quad m_0 \to Mass~of~empty~bottle \\\qquad m_1 \to Mass~of~bottle+liquid \quad V \to Volume$$ $$\text {iii)}\quad \rho = \frac {m}{V_1 - V_0}$$ $$\qquad \text {Where}~~\rho \to Density,\quad m \to Mass \\\qquad V_0 \to Initial~Volume,\qquad V_1 \to Final~Volume$$

Example 1

In an experiment to determine the density of liquid Y, Sophia a form IA student obtained the following; Mass of beaker is 500g, Mass of beaker and liquid is 600g and Volume of liquid is 25 cm³. Find the density

Solution

Data given

Mass of empty beaker (m₀) = 500 g

Mass of empty beaker + liquid (m₁) = 600 g

Volume (V) =25 cm³

Density (ρ) = ?

$$~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~\rho = \frac {m_1 - m_0}{V}$$ $$~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ = \frac {600 - 500}{25}$$ $$~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ = \frac {100}{25}$$ $$~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ = 4~g/cm^3$$

The density of liquid Y = 4 g/cm³

Example 2

The mass of a solid object with an irregular shape is 40 g. The solid object is totally immersed in water of volume 50 cm³ containing in a measuring cylinder rise to 70 cm³. Calculate density of the body

Solution

Data given

Mass (m) = 40 g

Initial Volume (V₀) = 50 cm³

Final Volume (V₁) = 70 cm³

Density (ρ) = ?

$$~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~\rho = \frac {40}{70 - 50}$$ $$~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ = \frac {40}{20}$$ $$~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ = 2~g/cm^3$$

The density of the body = 2 g/cm³