Question

The ratio of the C.G.S unit of pressure to the S.I unit of pressure is $10$.
A. True
B. False

Answer 1

Pressure is defined in two systems System international which is S.I. system as Pascal which is $1\text{Newton/}{{\text{m}}^{\text{2}}}$. In the centimeters, gram and second system (C.G.S) it is expressed as barye which is $1\,\text{dyne/c}{{\text{m}}^{2}}$.
Express both the units of pressure in standard measurable quantities which are kilograms, meters and seconds for the SI system and grams, centimeters and seconds for the C.G.S system and then take the ratio of both quantities.

Complete answer:
Pressure is defined as force acting on per unit area surface.it acts perpendicularly on the surface. It shows variation with height. when we go up in the atmosphere, its value decreases.
Formula for pressure=$\dfrac{Force}{area}$
The dimensional formula for pressure can be written from the formula for pressure,
Pressure$=\dfrac{ML{{T}^{-2}}}{{{L}^{2}}}$=$M{{L}^{-1}}{{T}^{-2}}$

Now we will put the values of mass length and time in both the standard systems which are C.G.S and S.I and take the ratio of both quantities.

Pressure in C.G.S system=$\dfrac{1g}{1cm\times {{s}^{2}}}$
Pressure in S.I system=$\dfrac{1kg}{1m\times {{s}^{2}}}$

Taking the ratio of above two quantities,
$\Rightarrow \dfrac{C.G.S}{S.I}=\dfrac{1g}{1cm}\times \dfrac{100cm}{1000g}$
$\Rightarrow \dfrac{C.G.S}{S.I}=\dfrac{1}{10}$
Hence the ratio of pressure in both the system of units is $\dfrac{1}{10}$.

Hence the statement given in question is false and I.e., B.

Note:
Other than S.I and C.G.S system, there are other system of units as well for measuring standard quantities:
1. F.P.S system-foot, pound and second system
2. M.K.S system-meter, kilogram and second system
The pressure is measured in reference to the height of some standard liquid which is taken as mercury.
The standard atmospheric pressure is measured as $760mm$ of mercury.