Question

A piece of coal sample weights 10 kg in air and 2kg when immersed in water (sp. gr. 1). the specific gravity of the coal sample is __

Answer 1

mass of coal in air = 10 kg

$\rho_{coal}V = 10 kg$

now when immersed in water

$(\rho_{coal} - \rho_w)*V = 2 kg$

now divide the two equations

$\frac{\rho_{coal} - \rho_{w}}{\rho_{coal}} = 5$

$1 - \frac{\rho_w}{\rho_{coal}} = \frac{1}{5}$

$\frac{\rho_w}{\rho_{coal}} = 1 - \frac{1}{5} = \frac{4}{5}$

specific gravity of coal is given by

$\frac{\rho_{coal}}{\rho_w} = \frac{5}{4}$

$\rho_{spe} = 1.25$

so the specific gravity will be 1.25