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

#### Solution

The S.I. unit of mass is kilogram (symbol kg) and of volume is

cubic metre (symbol m^{3}). Therefore S.I. unit of density is kg/m^{3}

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/cm^{3} or g cm^{-3}.

Relationship between kg `"m"^-3` and g `"cm"^-3`

1 kg = 1000 g

or 1 g = `1/1000` kg

and 1 `"m"^3 = (100 "cm")^3`

= 100 × 100× 100 `cm^3`

= 10,00,000 `cm^3`

or 1 `"cm"^3 = 1/1000000 "m"^3`

now 1 g `"cm"^-3 = (1 "g")/(1 "cm"^3)`

=`(1/1000 "kg")/(1/1000000 "m"^3)`

= `1000000/1000 "kg" "m"^-3`

= 1,000 kg `"m"^-3`

Thus , 1 g `"cm"^-3 = 1.000 "kg" "m"^-3`