Question

If an object has a density of \[8.65\dfrac{g}{{c{m^3}}}\] . What is its density in units of \[\dfrac{{kg}}{{{m^3}}}\] ?

Answer 1

Hint: In this question we have to do some basic unit conversion.
So, in this question we have to convert the density unit from the CGS system to the MKS system. So, we should know how to convert grams to kilograms and centimeters to meters.
$1000g = 1kg$
$100cm = 1m$
We will use it to solve this question.

Complete answer:
As given density = \[8.65\dfrac{g}{{c{m^3}}}\]
As we know
\[Density = \dfrac{{mass}}{{volume}}\]
So, here we have to convert
Unit of mass from gram to kg
As $1000g = 1kg$
So, $1g = \dfrac{1}{{1000}}kg$
\[voulme = lengt{h^3}\]
Unit of measurement from cm to m
As, $100cm = 1m$
So, $1cm = \dfrac{1}{{100}}m$
Keep this value in density = \[8.65\dfrac{g}{{c{m^3}}}\]
\[ \Rightarrow 8.65\dfrac{1}{{1000}} \times {\left( {\dfrac{{100}}{1}} \right)^3}\]
We will solve term inside the bracket,
\[ \Rightarrow 8.65\dfrac{1}{{1000}} \times \left( {\dfrac{{1000000}}{1}} \right)\]
\[ \Rightarrow 8.65 \times 1000 = 8650\dfrac{{kg}}{{{m^3}}}\]
So, we can write \[8.65\dfrac{g}{{c{m^3}}} = 8650\dfrac{{kg}}{{{m^3}}}\]

Note:
MKS system: The MKS system of units is a physical system of measurement that uses the meter, kilogram, and second (MKS) as base units. It forms the base of the International System of Units (SI).
CGS system: The centimetre–gram–second (abbreviated CGS or cgs) system of units is a variation of the metric system that uses the centimetre as the unit of length, the gram as the unit of mass, and the second as the unit of time. All CGS mechanical units are explicitly derived from these three foundation units, however the CGS system was extended in a variety of ways to include electromagnetism.