Question

What is the C.G.S. unit of density?
A) $gcm^{-3}$
B) $gm^{-3}$
C) $gcm^{-2}$
D) $kgm^{-3}$

Answer 1

Hint: C.G.S. is the abbreviation for Centimeter-Gram-Second. So, the name itself suggests what will be the unit of density. We will first use the formula of density and then will derive its unit.

Complete step by step solution:
In a C.G.S. or the Centimeter-Gram-Second is a type of metric system in which the unit of length, mass and time is taken as centimeter, gram and seconds respectively.
Since, density of an object is defined as the mass it has per unit of volume.
Mathematically, ${\text{density}}=\dfrac{\text{mass}}{\text{volume}}$, where the unit of the mass will be grams and the unit of the length will be centimeters.
Therefore, unit of density will be $\dfrac{g}{cm^3}=gcm^{-3}$

Hence, option A is the correct answer.

Additional information:
The C.G.S. system has largely been superseded by the MKS system which is the abbreviation of meter, kilogram and seconds which has also been replaced by the SI or the international system of units. In recent times, many fields of engineering involve the use of SI units while there are still many subparts, where the CGS system is still being used.
In measuring purely mechanical systems which involve the units such as length, mass, force, pressure and so on, the difference in these two units are very straightforward. The factors of conversion of units are all of powers of 10. Like 100cm = 1m and 1000g = 1kg etc.

Note: Not all the units in different systems change, like the unit of time is the same in the three systems of units and is measured in seconds. The CGS unit of density would have also been found out by converting its SI unit using proper unit conversion.