Question

Atmospheric pressure in SI units can be written as $1 \cdot 01325 \times {10^5}N{m^{ - 2}}$. Using the concept of dimensional analysis, its value in CGS unit will be expressed as
A. $1 \cdot 01325 \times {10^5}\dfrac{{dyne}}{{c{m^2}}}$
B. $1 \cdot 01325 \times {10^6}\dfrac{{dyne}}{{c{m^2}}}$
C. $1 \cdot 01325 \times {10^7}\dfrac{{dyne}}{{c{m^2}}}$
D. $1 \cdot 01325 \times {10^8}\dfrac{{dyne}}{{c{m^2}}}$

Answer 1

To solve this question, the SI unit should be analysed into the basic dimensional quantities. Once that has been done, the CGS equivalents of those basic dimensional quantities should be substituted in the dimensions to obtain the CGS units.
SI stands for System International units and CGS stands for Centimetre Gram and Second system.

Complete step-by-step answer:
The International System of Units has a set of seven basic quantities known as the fundamental quantities. They are:
A. Length
B. Mass
C. Second
D. Temperature
E. Current
F. Amount of substance
G. Luminous Intensity
The other physical quantities in nature are called derived quantities and they are derived from one or more of the above seven fundamental quantities.
Hence, any physical quantity can be expressed as a combination of these 7 basic quantities. This process is called dimensional analysis.
Let us perform the dimensional analysis on the given quantity pressure.
The SI unit for pressure is pascal (Pa)
Pressure is defined as the force per unit area.
$P = \dfrac{F}{A}$
A pascal is defined as a force of one newton per one metre-square area.
$1Pa = \dfrac{{1N}}{{1{m^2}}}$
Force is defined as the product of mass and the acceleration of the body.
$F = ma$
One newton is equal to the product of the mass of one kilogram and the acceleration of one metre per second squared.
$1N = 1kg \times 1m{s^{ - 2}}$
Thus,
$1Pa = \dfrac{{1kg \times 1m{s^{ - 2}}}}{{1{m^2}}}$
By converting the above units in CGS system, we get –
$1Pa = \dfrac{{1000g \times 100cm{s^{ - 2}}}}{{10000c{m^2}}}$
$\Rightarrow 1Pa = \dfrac{{{{10}^5}}}{{{{10}^4}}}gcm{s^{ - 2}}c{m^{ - 2}}$
The units $1gcm{s^{ - 2}} = 1dyne$ which is the CGS unit for force.
Thus,
$1Pa = 1N{m^{ - 2}} = 10dyne - c{m^{ - 2}}$
Given the atmospheric pressure is $1 \cdot 01325 \times {10^5}N{m^{ - 2}}$, to convert it to the units $dyne - c{m^{ - 2}}$, we have to multiply it by the value of 10.
Thus, the atmospheric pressure in CGS system, is – $1 \cdot 01325 \times {10^5}N{m^{ - 2}} \times 10 = 1 \cdot 01325 \times {10^6}dyne - c{m^{ - 2}}$

Hence, the correct option is Option B.

Note: Other than the SI and CGS systems, there is another unit of measurement known as FPS system (Foot, Pound and Second). In the FPS system, the pressure is measured in the unit called
psi (pounds per square inch).
The conversion is given as follows:
$1psi = 6894 \cdot 76Pa$
The standard atmospheric pressure in psi units is equal to = $14 \cdot 6959psi$