Question

The ratio of the CGS unit pressure to the SI unit of pressure is $10$. True or false?

Answer 1

Hint
The SI unit and CGS unit to be written in terms of force per area. Divide dyne per centimeter square with newton per meter square. Use the conversion factor between dyne with newton and centimeter with meter. Simplify to find the ratio.

Complete step-by-step solution
Pressure exerted is defined as the force exerted per unit area. It is given by,
$P = \dfrac{F}{A}$
The SI unit of pressure is the SI unit of force per area that is newton per meter square. $= N/{m^2}$
The CGS unit of pressure is the CGS unit of force per area that is dyne per centimeter square. $= dyne/c{m^2}$
The ratio of CGS unit to SI unit is given by,
$= \dfrac {dyne/{cm^2}}{N/{m^2}}$
We know that,
$1N = {10^5}dyne$
$1m = {10^2}cm$
Substitute this value in place of newton and meter square.
$\dfrac{{dyne}}{{c{m^2}}} \times \dfrac{{{{10}^4}c{m^2}}}{{{{10}^5}dyne}} = \dfrac{1}{{10}}$
Therefore, the ratio of CGS unit to SI unit of pressure is $\dfrac{1}{{10}}$ .
Hence, the statement is false.

Note
SI system is known as the international system of units and its extended system of units is applied to whole physics. There are seven quantities in this system.
The CGS system is also called the Gaussian system. The fundamental quantities length, mass and time are centimeter, grams and seconds.