Question

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

Answer 1

- Hint: SI unit of volume is $m^3$ and CGS unit of volume is $c{m}^3$, convert metre into centimetre or centimetre into metre by using the formula, $1m=100cm$ ,then take the ratio of the CGS unit to the SI unit to find whether the given statement is true or false.

Formula used - $1m=100cm$

Complete step-by-step solution -
The SI unit means System International unit, which uses metres, kilograms and seconds for length, mass and time. It is also called the MKS system.
Whereas, the CGS system uses centimetres, grams and seconds for length, mass and time.
We know that the CGS unit of volume is $c{m}^3$ .
Also, the SI unit of volume is $m^3$.
Now, ratio of CGS unit of volume to that of SI unit of volume ` $={\displaystyle \frac{c{m}^3}{m^3}}$
Now we know that $1m=100cm$
So, we can write that $1m^3=(100cm{)}^3={10}^{6}c{m}^3$
Putting this in the ratio we get-
Ratio of CGS unit of volume to the SI unit of volume $={\displaystyle \frac{c{m}^3}{{10}^{6}c{m}^3}}={\displaystyle \frac{1}{{10}^6}}$
Therefore, we can say that the given statement is true.

Note – Whenever such types of questions appear then first define what is the SI unit and then what is the CGS system of the unit. As mentioned in the solution, SI unit of volume is $m^3$ and CGS unit of volume is $c{m}^3$, and then taking the ratio of CGS unit of volume to SI unit of volume, and then substituting $1m^3=(100cm{)}^3={10}^{6}c{m}^3$ , we found the ratio and found out that the given statement is true. Always keep in mind that the CGS and SI units are different, so you should know the basic formulas to convert one unit into another unit.