Question

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

Answer 1

The S.I. unit of mass is kilogram (symbol kg) and of volume is
cubic metre (symbol m³). Therefore S.I. unit of density is kg/m³
or kg m^-3.
The C.G.S. unit of mass is gram (symbol g) and of volume is cubic centimetre (symbol cm3). Therefore the C.G.S. unit of
density is g/cm³ or g cm^-3.

Relationship between kg ${\displaystyle {\text{m}}^{-3}}$ and g ${\displaystyle {\text{cm}}^{-3}}$

1 kg = 1000 g 

or 1 g = ${\displaystyle \frac{1}{1000}}$ kg 

and 1 ${\displaystyle {\text{m}}^3={\left(100\text{cm}\right)}^3}$

                      = 100 × 100× 100 ${\displaystyle c{m}^3}$

                      = 10,00,000 ${\displaystyle c{m}^3}$

or 1 ${\displaystyle {\text{cm}}^3=\frac{1}{1000000}{\text{m}}^3}$ 

now  1  g ${\displaystyle {\text{cm}}^{-3}=\frac{1\text{g}}{1{\text{cm}}^3}}$

=${\displaystyle \frac{\frac{1}{1000}\text{kg}}{\frac{1}{1000000}{\text{m}}^3}}$

= ${\displaystyle \frac{1000000}{1000}\text{kg} {\text{m}}^{-3}}$

= 1,000 kg ${\displaystyle {\text{m}}^{-3}}$

Thus , 1 g ${\displaystyle {\text{cm}}^{-3}=1.000 \text{kg} {\text{m}}^{-3}}$