Question

The density of water in the C.G.S. system is $1\,g/c{m^3}$. Find its value in the SI system dimensionally.

Answer 1

The SI units of density is $kg/{m^3}$. We need to convert the units of grams to kilograms and centimeters to meters and calculate the value of density in SI units.

Complete step by step answer
We’ve been given the density of water as $1\,gm/c{m^3}$. Now, we know that the units of density in the SI unit system is given as $kg/{m^3}$. So, let's convert each individual quantity to their respective SI units.
We know that mass of $1\,kg = 1000\,g$. So, we can write
$1g = 0.001\,kg$
Now, for the quantity of length, we have
$1\,m = 100\,cm$. So, we can write,
$1\,cm\, = \,0.01\,m$
Now as density is given as $1\,gm/c{m^3}$, we can calculate the density of water in the I unit system which uses the unit’s kilograms and meters as
${\text{Density = 1g/c}}{{\text{m}}^3}{\text{ = }}\dfrac{{0.001}}{{{{(0.01)}^3}}}kg/{m^3}$
${\text{Density = }}1000\,kg/{m^3}$
Hence the value of density of water in SI units is $1000\,kg/{m^3}$.

Additional information
The SI unit system is the standard unit of measurement consisting of 7 quantities which is a set of quantities from which any other quantity can be derived and used internationally as a common unit system. The units and their physical quantities in the SI unit system are the second for time, the meter for measurement of length, the kilogram for mass, the ampere for electric current, the Kelvin for temperature, the mole for amount of substance, and the candela for luminous intensity.

Note
The density can be measured in any unit system provided we know the conversion of the base units in the new system which is the SI unit system in this case. The actual density of water varies depending on the amount of different chemicals in the water actually as well on the temperature of the water.