Question

The density of water is equal to
A. $10^{-3} kgm^{-3}$
B. $10^{-2} kgm^{-3}$
C. $10^{2} kgm^{-3}$
D. $10^{3} kgm^{-3}$

Answer 1

Hint: The density of water is taken to be 1 in many examples of relative density calculations. It is for the case of c. g. s. units that the density of water is 1 grams per c.c. (or $cm^3$). We can remember this can convert to S.I. units for this question.

Complete answer:
Density of any substance is given as its mass divided by its volume.
$density = \dfrac{mass}{volume}$
In various applications, the density of water as compared to other objects is written as 1 gm/$cm^3$.
To convert this into S.I., we will use the relations:
$1 g = 10^{-3} kg$
$1 cm = 10^{-2} m$
for the case of $cm^3$ we can write:
$1 cm^3 = 10^{-6} m^3$

Therefore,
$1 \dfrac{gm}{cm^3} = \dfrac{10^{-3} kg}{10^{-6} m^3}$
Or,
$1 \dfrac{gm}{cm^3} = 10^{3} \dfrac{ kg}{m^3}$

So, the correct answer is “Option D”.

Additional Information:
The relative density of a substance with respect to water is:
Relative density = density of substance/ density of water.
Since the density of water is 1 g per c.c., we can easily find out the relative density. This greatly helps in determining if the other substance will float or will sink in water (like oil or honey). Density of water is a standard for measurement. Along will this, freezing and boiling points of water are also standard for measurement. It is not a coincidence that the freezing point is 0$^{\circ}$ and boiling point is 100$^{\circ}$. It has been kept here, to ease out the calculations.

Note:
Here or in calculations like this when it is required to convert $cm^3$ to $m^3$, one might not account for the power. In a hurry, mathematical errors might occur.
It is better to note down the units first and then write their conversions separately and then add the powers wherever required.