Question

What is the density of water?
${\text{A}}{\text{.}}$ 1000 kg/${{\text{m}}^3}$
${\text{B}}{\text{.}}$ 1 kg/${{\text{m}}^3}$
${\text{C}}{\text{.}}$ 1000 kg/${\text{c}}{{\text{m}}^2}$
${\text{D}}{\text{.}}$ 100 kg/${{\text{m}}^3}$

Answer 1

Hint: Here, we will proceed by defining the density of any substance. Then, we will express the density mathematically. Then, we will give the S.I unit and dimension of density. Finally, we will write down the density of water.

Complete step-by-step answer:

Density of any substance can be defined as the mass of that substance per unit volume of that substance. Density of any material is simply the ratio of the mass of the material to the volume of the material.
Mathematically, density of any substance can be expressed as

Density = $\dfrac{{{\text{Mass}}}}{{{\text{Volume}}}}$

As we know that the S.I unit of mass is kilogram (kg) and the S.I unit of volume is cubic metre (${{\text{m}}^3}$). So, we can say that the S.I unit of density is kg/${{\text{m}}^3}$.

Also, the dimension of mass is [M] and the dimension of volume is
$\left[ {{{\text{L}}^3}} \right]$.
So, the dimension of the density is given by

Dimension of density = $\dfrac{{{\text{Dimension of mass}}}}{{{\text{Dimension of Volume}}}} = \dfrac{{\left[ {\text{M}} \right]}}{{\left[ {{{\text{L}}^3}} \right]}} = \left[ {\text{M}} \right]\left[ {{{\text{L}}^{ - 3}}} \right] = \left[ {{\text{M}}{{\text{L}}^{ - 3}}} \right]$
Therefore, the dimension of density is $\left[ {{\text{M}}{{\text{L}}^{ - 3}}} \right]$.

Density is a physical quantitative attribute of a material or of a more or less stable mixture. When we take a piece of a material, it has some mass and volume. The mass divided by volume is called density, and it depends solely on substance (remains the same for different parts of the same material).

Saltwater (like oceans) has a different density that depends on how much salt the water dissolves. The density of seawater is usually slightly higher than that of fresh water.
Density of water is taken as 1000 kg/${{\text{m}}^3}$. This value of the density of water (i.e., 1000 kg/${{\text{m}}^3}$) signifies that there is 1000 kg mass of the water present in 1 ${{\text{m}}^3}$ volume of the water.

As we know that 1 m = 100 cm $ \Rightarrow 1{\text{ }}{{\text{m}}^3} = {\left( {100} \right)^3}{\text{ c}}{{\text{m}}^3} = {10^6}{\text{ c}}{{\text{m}}^3}$

Density of water = 1000 kg/${{\text{m}}^3}$ = $\dfrac{{1000}}{{{{10}^6}}} = \dfrac{1}{{1000}}$ kg/${\text{c}}{{\text{m}}^3}$

Therefore, option A is correct.

Note: Since, the density of water is 1000 kg/${{\text{m}}^3}$ because of this in the evaluation of the specific gravity of any other liquid (except water), water is taken as the standard liquid. The specific gravity of any liquid is defined as the ratio of the density of that liquid to the density of the water.