Question

State the S.I. and C.G.S. units of density. How are they interrelated?

Answer 1

S.I. and C.G.S. units of density:

• The density of a substance is defined as the mass of a unit volume of that substance.

$\text{Density}\left(d\right)=\frac{\text{mass}\left(m\right)}{\text{volume}\left(V\right)}$

• The S.I. unit of mass is kilogram (𝑘𝑔) and of volume is cubic metre $\left(m^3\right)$.
• Therefore S.I. unit of density is $kg{m}^{-3}$ .
• The C.G.S. unit of mass is gram (g) and of volume is cubic centimetre $\left(c{m}^3\right)$.
• Therefore the C.G.S. unit of density is $gc{m}^{-3}$.

Relation between $kg{m}^{-3}$and $gc{m}^{-3}$:
Since, 1 𝑘𝑔 = 1000 𝑔
and $1m^3=(100{)}^{3}c{m}^3$
$={10}^{6}c{m}^3$
So, $1kg{m}^{-3}=\frac{1000g}{{10}^{6}c{m}^3}$
$=\frac{1gc{m}^{-3}}{1000}$
Hence, $1gc{m}^{-3}=1000kg{m}^{-3}$