Question

To convert density of $kg{{m}^{-3}}$ into $gc{{m}^{-3}}$, we divide quantities with
(A) 100
(B) 10
(C ) 200
(D) 1000

Answer 1

Hint: One kilogram equals to 1000g and one metre is equal to 100cm. By substituting these two values we can convert density in terms of gram per cubic centimeter. Where density can be described as the ratio of mass per unit metre.

Complete step-by-step solution:
We know that one kilogram equals 1000g and one metre is equal to 100cm.
That is,
$1kg=1000g$
$1m=100cm$
Substituting these values we get,
 $\begin{align}
  & 1\frac{kg}{{{m}^{3}}}=1\times 1000g\times \frac{1}{{{10}^{6}}c{{m}^{3}}} \\
 & \Rightarrow 1\frac{kg}{{{m}^{3}}}=\frac{1}{1000}\frac{g}{c{{m}^{3}}} \\
\end{align}$
Hence if we divide the quantities with 1000 we can convert kilogram per cubic metre into gram per cubic metre.
Therefore the correct option is (D).

Note: The density of a material depends on the variation of temperature and pressure. Volume of the object decreases with increasing pressure. The SI unit of pressure is kilogram per cubic metre. That is density can be described as the ratio of mass per unit metre. Commonly expressed unit of density is gram per cubic centimeter. Thus we can say that density depends on two factors. That is, the mass of the object and its volume.
There are 7 basic units of measurement. They are length, time, amount of substance, electric current, temperature, luminous intensity and mass. The conversion process depends on the situation and the purpose of conversion. For every measurement the precision and accuracy has great importance. Nowadays there are many software tools available for the conversion of one unit to another.