Question

What is the density of water?
A) $1000{\text{gc}}{{\text{m}}^{ - 3}}$
B) $1{\text{kg}}{{\text{m}}^{ - 3}}$
C) $1{\text{gc}}{{\text{m}}^{ - 3}}$
D) None of these

Answer 1

Hint:The density of a substance refers to the mass of some substance per unit volume. This suggests that the density of a substance is essentially a relationship between the mass of the substance and the volume occupied by the substance. The density of a material describes how tightly packed the matter in the material is. Solids are usually denser than liquids and gases.

Complete step by step answer.
Step 1: Express the density of water in its S.I unit.
The density of water refers to the weight of water per its unit volume. The volume depends on the temperature of the water. The general relation for the density of a substance is expressed as $\rho = \dfrac{m}{V}$ where $m$ is the mass of the substance and $V$ is the volume of the substance.
The S.I unit of density is kilogram per cubic meter. The density of water in its S.I unit is $\rho = 1000{\text{kg}}{{\text{m}}^{ - 3}}$ which means that $1000{\text{kg}}$ of water occupies a volume of $1{{\text{m}}^3}$.
The given options include values of density represented in the units of gram per cubic centimetre.
So if we were to convert the density $\rho = 1000{\text{kg}}{{\text{m}}^{ - 3}}$ into gram per cubic centimetre then we obtain $\rho = \dfrac{{1000 \times {{10}^3}}}{{1 \times {{10}^6}}} = 1{\text{gc}}{{\text{m}}^{ - 3}}$ --------- (1)

Thus the correct option is C.

Note:We know that $1{\text{kg}} = 1000{\text{g}} = {10^3}{\text{g}}$ . This conversion from kilogram to gram is applied in equation (1). The conversion relation from meter to centimetre is $1{\text{m}} = 100{\text{cm}} = {10^2}$ , then we have $1{{\text{m}}^3} = {\left( {{{10}^2}} \right)^3}{\text{c}}{{\text{m}}^3} = {10^6}{\text{c}}{{\text{m}}^3}$ . This conversion relation is used in equation (1). Water does not have an absolute value for density. This is because its density depends on its temperature. Cooling water from room temperature to $4^\circ {\text{C}}$ will increase its density. If the temperature is again decreased, its density decreases. This is why we say water is denser than ice.