Question

What is the unit of relative density?
A. $gc{{m}^{-3}}$
B. $kg{{m}^{-3}}$
C. ${{m}^{3}}k{{g}^{-1}}$
D. no unit

Answer 1

Hint: When there is a relative word it means we need to define quantity with respect to each other. And when there are two same quantities in ratio then there is no unit for ratio.

Complete step by step answer:
In general relative density is defined as ratio of density of substance to the density of reference material. So we can say relative density is a ratio of two same quantities. Hence it is unit less quantity. Every substance has different density. It is also known as specific gravity.
$\operatorname{Re}lative\,\,density\,=\,\dfrac{density\,of\,subs\tan ce}{density\,of\,a\,reference\,material}$
In the case of liquid we consider water as reference material having density $1000\,kg/{{m}^{3}}$ and in the case of gases we consider air as standard material having density $1.225kg/{{m}^{3}}$ Generally density is defined as ratio of mass to volume. Where SI unit of mass is kg and SI unit of volume is $meter^{3}$. Hence SI unit of density is \[kg/{{m}^{3}}\].
As we know the density of mercury is $13.6\,kg/{{m}^{3}}$ and the density of water which is standard fluid or reference fluid is $1\,kg/{{m}^{3}}$. So the relative density (specific gravity) of mercury is 13.6. It means mercury is heavier than water. Same as well the density of petrol is $0.786\,kg/{{m}^{3}}$, so the relative density(specific gravity) of petrol is .786 it means petrol is lighter than the water.

So, the correct answer is “Option D”.

Note:
If the length of rod 1 is 10 cm and length of rod 2 is 20 cm then ratio of length of rod 1 to rod 2 is $\dfrac{10\,cm}{20\,cm}=1:2$
So we can see that the ratio of the same quantities is unit less.