Question

The relative density of aluminium is $2.7$. What is the density of aluminium in SI Units? (Density of water $ = 1.0 \times {10^3}kg/{m^3}$)
A) $2700kg/{m^3}$
B) $270kg/{m^3}$
C) $27kg/{m^3}$
D) $2.7kg/{m^3}$

Answer 1

Hint: The relative density of any substance is defined as the ratio of the density of the substance to the density of a specific reference material, which is mainly taken as water at ${4^ \circ }C$. As you can see, the relative density is a ratio, hence it has no units.

Formula Used:
If the density of a substance is ${\rho _s}$ and the density of water is ${\rho _w}$ , then the relative density ${\rho _{rel}}$ of that substance can be defined as
${\rho _{rel}} = \dfrac{{{\rho _s}}}{{{\rho _w}}}$

Complete step by step answer:
Given:
The relative density of aluminium is $2.7$.
The density of water in SI units is $1.0 \times {10^3}kg/{m^3}$
To get: The density of aluminium in SI units.
Step 1:
Express the density of the substance ${\rho _s}$ from the eq (1).
$
  {\rho _{rel}} = \dfrac{{{\rho _s}}}{{{\rho _w}}} \\
   \Rightarrow {\rho _s} = {\rho _{rel}} \times {\rho _w} \\
 $

Step 2:
Now put the values to calculate the density of the aluminium ${\rho _{al}}$ from eq (1)
$
  {\rho _{al}} = {\rho _{rel}} \times {\rho _w} \\
   \Rightarrow {\rho _{al}} = 2.7 \times 1.0 \times {10^3}kg/{m^3} \\
   = 2700kg/{m^3} \\
 $
Final Answer:
The density of aluminium in SI units is (A) $2700kg/{m^3}$.

Additional Information:
The temperature dependence of the density of the materials affects relative density. So, it is required to note the temperature and pressure of both the target and the reference substance while comparing. General reference material used is water at ${4^ \circ }C$. Relative Density can help to predict the buoyancy of a material. A substance with specific density greater than 1, sinks in the reference material. It is also called Specific Gravity.

 Note: To calculate relative density you need to be careful about what is taken as the reference material. If nothing is stated separately, then it is customary to take the reference material as water.