Question

(a) What is the difference between the density and relative density of a substance?
(b) If the relative density of a substance is $7.1$ , what will be its density in SI units?

Answer 1

Hint : In Physics density is a very basic concept and it can be defined as the mass per unit volume. It is denoted by row ( $\rho$ ). It is commonly measured in gram per centimetre cube. Here we will use the formula - $\rho = \dfrac{M}{V}$ where M is the mass and V is the volume.

Complete Step By Step Answer:
The density of the substance can be defined as the ratio of the mass of the substance per unit volume.
Density of substance $= \dfrac{{Mass{\text{ of substance}}}}{{Volume{\text{ of Substance}}}}$
SI (Standard International) unit of density can be given as $kg/{m^3}$
The Relative density of the substance can be defined as the ratio of the density of the substance with the density of the water.
Relative density of the substance $= \dfrac{{Density{\text{ of substance}}}}{{Density\;of{\text{ Water}}}}$
Common units from the numerator and the denominator cancel each other.
Therefore, the relative density of the substance has no units.
b.) Relative density of the substance $= \dfrac{{Density{\text{ of substance}}}}{{Density\;of{\text{ Water}}}}$
Place the given values in the above equation –
$7.1 = \dfrac{{Density{\text{ of substance}}}}{{1000{\text{ kg/}}{{\text{m}}^3}}}$
Do cross multiplication, where the numerator of one side is multiplied with the denominator of the opposite side and make the required term the subject –
Density of the substance $= 7.1 \times {10^3}\;{\text{kg/}}{{\text{m}}^3}$
This is the required solution.

Note :
Remember the basic standard formulas to solve these types of questions. Always check the given units and the units asked in the solution. All the units should be in the same format. Since here all the units were given in the MKS (Metre kilogram Second) system of units it was just the substitution of values in the formula.