Question

The density of a piece of clay is $1.8$ in $CGS$ system of units. The corresponding value in $SI$ unit system is:
A) $18000$
B) $1800$
C) $180$
D) $18$

Answer 1

The units are the terms that help us to compare the one quantity or the measurement with the other. Based on the location and their convenience, there are many classification of the system of units. They include $CGS$ , $SI$ , $FPS$ etc.

Useful formula:
The density is written as
$D = \dfrac{m}{V}$
Where $D$ is the density of the clay, $m$ is the mass of the clay and the $V$ is its own volume.

Complete step by step solution:
The expansion of the $CGS$ system of units is the centimeter gram and the second. The expansion of the $SI$ unit system is the standard system of units. In which the meter, kilogram and the second is used.
By using the formula of the density, the cgs system of the unit is calculated.
$D = \dfrac{m}{V} = gc{m^{ - 3}}$
It is given that the density of the clay in $CGS$ is $1.8\,gc{m^{ - 3}}$ .
By converting it to a $SI$ system of units, the gram changes to kilogram and the centimeter changes to the meter. Hence the unit of the density becomes,
$D = \dfrac{{1.8 \times {{10}^{ - 3}}\,Kg}}{{{{\left( {{{10}^{ - 2}}} \right)}^3}\,{m^3}}}$
By simplifying the above step,
$D = \dfrac{{1.8 \times {{10}^{ - 3}}\,Kg}}{{\left( {{{10}^{ - 6}}} \right)\,{m^3}}}$
By further simplification,
$D = 1.8 \times {10^3}\,Kg{m^{ - 3}}$
$D = 1800\,Kg{m^{ - 3}}$
Hence the value of the density in the $SI$ system of units is $1800\,Kg{m^{ - 3}}$ .

Thus the option (B) is correct.

Note: The units are mainly classified into fundamental units and derived units. The fundamental units are the basic units where the derived units are developed from the basic fundamental units. The density of the clay is the derived units, it is derived from the basic units like kilogram and the meter.