Worked Examples on Archimedes Principle

Considered Formula

$$\text {i)}\quad R.D = \frac {W_a - W_l}{W_a - W_w}$$ $$\qquad \text {Where}~~R.D \to Relative~density,\quad W_a \to Weight~in~air \\\qquad W_l \to Weight~in~liquid, \qquad W_w \to Weight~in~water$$ $$\text {ii)}\quad R.D = \frac {\rho_s}{\rho_w}$$ $$\qquad \text {Where}~~R.D \to Relative~density,\quad \rho_s \to Density~of~substance \\\qquad \rho_w \to Density~of~water$$

Example 1

A piece of glass weight in air 1.2N and 0.7N when completely immersed in water calculate it’s.

a)    Relative density

b)    Density of glass

c)     Volume of glass

(Density of water = 1g/cm³)

Solution

Data given

Weight in air (W_a) = 1.2 N

Weight in water (W_w) = 0.7 N

Density of water (ρ_w) = 1g/cm³

a)        Relative density (R.D) = ?

$$~~~~~~~~~~~~~~~~~~~~~~~~~~~~R.D = \frac {W_a}{W_a - W_w}$$ $$~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ = \frac {1.2}{1.2 - 0.7}$$ $$~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ = \frac {1.2}{0.5}$$ $$~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ = \frac {1.2 \times 10}{0.5 \times 10}$$ $$~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ = \frac {12}{5}$$ $$~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ = 2.4$$

          The relative density = 2.4

b)  CONTINUE READING