Question

Density of liquid in the CGS system is $0.625\,gc{m^{ - 3}}$. What is its magnitude in the SI system?
A. $0.625$
B. $0.0625$
C. $0.00625$
D. $625$

Answer 1

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

Complete step by step solution:
We’ve been given the density of liquid as $0.625\,gc{m^{ - 3}}$. Now, we know that the units of density in the SI unit system are given as $kg/{m^3}$. Let's convert each individual quantity to their respective SI units. We know that mass of $1\,kg = 1000\,g$. So, we can write:
$0.625\,g = 0.000625\,kg$

Now, for the quantity of length $1\,m = 100\,cm$, So, we can write:
$1\,cm = 0.01\,m$
Now as density is given as $0.625\,gc{m^{ - 3}}$, we can calculate the density of water in the I unit system which uses the unit’s kilograms and metres as,
$\text{Magnitude} = 0.625\,g/c{m^3} \\$
$\Rightarrow \text{Magnitude} = \dfrac{{0.000625}}{{{{(0.01)}^3}}}kg/{m^3} \\$
$\therefore \text{Magnitude} = 625\,kg/{m^3}$
Therefore, the magnitude of the density of liquid in the SI system is $625\,kg/{m^3}$.

Thus, the correct option is C.

Additional information: The SI unit system, which is used globally as a common unit system, is the standard unit of measurement made up of a set of numbers from which any other quantity may be derived. The second for time, the metre for length, the kilogramme for mass, the ampere for electricity, the kelvin for temperature, the mole for substance amount, and the candela for luminous intensity are the units and their physical quantities in the SI unit system.

Note: Any unit system can be used to measure density as long as we are aware of how to convert the base units to the new system, in this case the SI unit system. The amount of various compounds a liquid contains as well as its temperature affect the liquid's density in real life.