Question

What is the density of water in $kg{{m}^{-3}}$?
$\begin{align}
  & \text{A}\text{. 1} \\
 & \text{B}\text{. 1000} \\
 & \text{C}\text{. 100} \\
 & \text{D}\text{. 10000} \\
\end{align}$

Answer 1

Hint: If a substance of mass M occupies a volume V then its density will be the ratio of its mass to volume. Density can be expressed in various units. $kg{{m}^{-3}}$ is the SI unit of density. In the CGS system, the density of water is unity.

Complete step by step answer:
The density of any substance is defined as the ratio of its mass to volume. It is the measure of how dense a given material or substance is. That is, how much mass is concentrated in a unit volume. It is generally denoted by the symbol $\rho $
Therefore,
$\text{Density =}\dfrac{\text{Mass}}{\text{Volume}}$
The SI unit of mass is kg and the SI unit of volume is ${{m}^{3}}$, therefore, the SI unit of density will be $kg{{m}^{-3}}$
Dimensions of density:
$[\rho ]=[{{L}^{3}}{{M}^{1}}{{T}^{0}}]$
Approximately 1000kg of water occupies $1{{m}^{3}}$ of volume, therefore, the density of the water is $1000kg{{m}^{-3}}$

Answer - B. 1000

Additional Information:
A more commonly used unit of density is $gc{{m}^{-3}}$. It is a CGS unit of density.
$1kg{{m}^{-3}}=1\times {{10}^{3}}\times {{({{10}^{2}})}^{-3}}gc{{m}^{-3}}={{10}^{-3}}gc{{m}^{-3}}$
Therefore, the density of water in CGS units is $1000\times {{10}^{-3}}gc{{m}^{3}}=1gc{{m}^{3}}$

Factors affecting density:
1. Temperature:
The mass of a substance is always constant unless you add or remove some amount into it. But the volume can be changed. The volume of the substance increases or decreases when we heat or cool it. It means density can change when we change the temperature of a substance. In the case of water, the density of water increases as we decrease its temperature for all the substances except for water. Water shows anomalous behavior. As the temperature decreases the density of the water increases, reaches a maximum value, and then decreases. Thus, ice is less dense than liquid water.

2. Pressure:
If you increase the pressure, the substance gets compressed and more mass can be occupied in a smaller volume. Therefore, with the increase in pressure, density also increases.

Note:
Density plays an important role in many applications. Just like a nail made up of iron will sink in water but a ship made up of the same iron won’t sink. If you increase the volume of a given substance then you can decrease its density. Substances having less density than water will float on the surface of the water, whereas substances having more density than water will sink in water. Substances having densities equal to the density of water will float on the water.