Question

The density of copper is \[8.83gm\,c{{m}^{-3}}\]. Its value in the SI system is \[X\,kg\,{{m}^{-3}}\]. Find \[X\]
(A). \[8800\]
(B). \[8830\]
(C). \[8990\]
(D). \[8888\]

Answer 1

Hint: Determine the relationship between units in CGS and SI system. Use these relationships to convert from one unit to the other required unit. If converting from a smaller unit to a larger unit, divide the terms. If converting from a larger unit to a smaller unit, multiply the terms
Formulas Used:
 \[d=\dfrac{M}{V}\]
\[1\,kg=1000\,gm\]
\[1\,m=100\,cm\]

Complete answer:
Density is defined as mass per unit volume.
\[d=\dfrac{M}{V}\]
Here, \[d\] is density
\[M\] is mass. Its SI unit is \[kg\]
 \[V\] is volume. Its SI unit is \[{{m}^{3}}\]
Therefore the SI unit of density is \[kg\,{{m}^{-3}}\]
 We know
\[1\,kg=1000\,gm\] - (1)
\[1\,m=100\,cm\] - (2)
\[\therefore \,1\,{{m}^{3}}\,=100\times 100\times 100\,c{{m}^{3}}={{10}^{6}}\,c{{m}^{3}}\]
By convention, when we convert a smaller quantity to a larger quantity, we divide.
Therefore converting from a smaller CGS system to a larger SI system,
 \[\begin{align}
  & \dfrac{\dfrac{8.83\times 1}{1000}}{\dfrac{1}{{{10}^{6}}}} \\
 & \Rightarrow 8.83\times {{10}^{3}}=8830 \\
\end{align}\]
The copper density calculated in the SI system is \[8830\].

So the correct option is (B).

Additional Information:
The SI system or the International system of units is the only system which is used in nearly every country. It is also called the modern form of metric system. The \[7\] base units are metre (\[m\], length), kilogram (\[kg\], mass), - second (\[s\], time), kelvin (\[K\], temperature), mole (\[mol\], amount of substance), ampere (\[A\], electric current), candela (\[cd\], luminous intensity).

Note:
The CGS system or the centimeter-gram-second system of units is a form of metric system based on using centimeters as unit of length, gram as unit of mass and second as unit of time. The prefix of centi is used before units to denote \[\dfrac{1}{100}th\]part of a unit. Other prefixes are kilo, hecto, deca, deci, centi, milli.