Question

The ratio of CGS unit of volume to that of SI unit of volume is $\dfrac{1}{{{10}^{6}}}$
A) True
B) False

Answer 1

Hint: Define the CGS and SI unit of system. Obtain the units we use for volume in both CGS and SI units. Obtain the conversion formula from CGS unit to SI unit or vice-versa. Put these values in the unit of volume to find the conversion of the unit of volume.

Complete step by step answer:
CGS system is a system of units where we use cm as unit of length, gram as unit of mass and second as the unit of time.
Si unit or International system of units is a system of units based on the meter, kilogram, second, ampere, kelvin, candela and mole. We also have a set of prefixes to indicate the multiplication and division by a power of ten.
Volume of an object can be defined as the space occupied by the object or the space contained within a container.
The SI unit of volume is cubic meter or ${{m}^{3}}$.
A meter cube can be simply defined as the volume occupied by a cube of side one meter each.
CGS unit of volume is $c{{m}^{3}}$.
We know that the conversion from meter to cm is given as, $1m=100cm$
Ratio of CGS unit to SI unit $=\dfrac{c{{m}^{3}}}{{{m}^{3}}}=\dfrac{c{{m}^{3}}}{{{100}^{3}}c{{m}^{3}}}=\dfrac{1}{{{10}^{6}}}$ $$$$
Thus, the given statement is true.
The correct option is (A).

Note: Dimension of volume is $\left[ {{\text{L}}^{3}} \right]$. Volume expresses the amount of space that an object occupies. It is determined by other measurements of length which is a fundamental quantity. So, it is called a derived unit. Every measuring system that exists defines a unit volume for that system. Any unit of length gives a corresponding unit of volume. Barrels, bushels, drams, gills, pecks, teaspoons, cubic inch, cubic foot and other units are used in the empirical system. Cubic metre, litre, cubic centimetre and other units are used in SI systems.