Question

The unit of density in MKS and CGS system respectively are:
A. \[\text{kg/}{{\text{m}}^{\text{3}}}\text{ and g/c}{{\text{m}}^{\text{3}}}\]
B. \[\text{g/c}{{\text{m}}^{\text{3}}}\text{ and kg/}{{\text{m}}^{\text{3}}}\]
C. \[\text{g/c}{{\text{m}}^{\text{3}}}\text{ and kg/}{{\text{m}}^{2}}\]
D. \[\text{kg/c}{{\text{m}}^{2}}\text{ and g/}{{\text{m}}^{2}}\]

Answer 1

Hint: Recall the formula for density \[(\rho )\] i.e., density is defined as the mass per unit volume of a substance. Mathematically it is given by,
\[\text{Density( }\!\!\rho\!\!\text{ ) = }\dfrac{\text{mass(m)}}{\text{volume(V)}}\]

Complete step by step answer:

As we know that the density \[(\rho )\] is defined as mass per unit volume of a substance.
Density is the measure of how tightly packed and how heavy the molecules are present in an object. Density is the amount of substance within a certain volume.
Density is given by the formula,
\[\text{Density( }\!\!\rho\!\!\text{ ) = }\dfrac{\text{mass(m)}}{\text{volume(V)}}\]
On writing the unit of density in M.K.S. system, we have
The unit of density = \[kg/{{m}^{3}}\]
Again, on writing the unit of density in C.G.S. system, we have
The unit of density = \[g/c{{m}^{3}}\]
So, the units of density in M.K.S. and C.G.S systems are respectively \[kg/{{m}^{3}}\] and \[g/c{{m}^{3}}\].
Hence, the correct option is A, i.e., \[\text{kg/}{{\text{m}}^{\text{3}}}\text{ and g/c}{{\text{m}}^{\text{3}}}\].

Additional Information:
Relative Density: Relative density (R.D.) of a substance is the ratio of the density of the substance to the density of water at 4°C. i.e., \[{{\rho }_{r}}=\dfrac{{{\rho }_{subst.}}}{{{\rho }_{water}}}\]
It is also defined as the ratio of the mass of the substance to the mass of an equal volume of water at 4°C. Relative density (R.D.) has no unit.

Note: Students should understand both the systems of measurement i.e., M.K.S. and C.G.S. and they should memorize the units of basic physical quantities in both systems. Students need to know the formula for density of the substance so that they can find out its unit simply, by putting units of basic physical quantities.