Question

The pressure of ${10^3}$ $dyne/c{m^2}$ is equivalent to:
A. $10N/{m^2}$
B. ${10^2}N/{m^2}$
C. ${10^{-2}}N/{m^2}$
D. ${10^{-1}}N/{m^2}$

Answer 1

Hint: We need to convert CGS unit of pressure to pressure in S.I. units. $1\,Newton = 1kgm/{s^2}$ and $1 dyne= 1gcm/{s^2}$. $1kg = 100g; 1m = 100cm$ and seconds-s remains the same. We use these relations to obtain the required equivalent value

Complete step by step answer:
CGS unit: Here, C stands for centimeters, G stands for gram and S stands for seconds. Length is measured in centimeters; mass is measured in grams and time in seconds. Abbreviations used for centimeters is cm, a gram is gm, seconds is sec.
MKS system of units: Here, M stands for meters, K stands for the kilogram and S stands for seconds. Length is measured in meters; mass is measured in kilogram and time in seconds. Abbreviations used for meters is m, the kilogram is kg, seconds is sec.
This MKS system was later on extended to the S.I. unit.
S.I. unit: Internationally accepted system of units.
Pressure in terms of CGS unit: $dyne/c{m^2}$
Pressure in terms of S.I. unit: $Newton/{m^2}$
Pressure: It is defined as the amount of force per unit area of an object.
$Pressure = $$\dfrac{{Force}}{{Area}}$
=> CGS unit of force is ‘dyne’ and S.I. the unit is Newton.
1 newton force: When a force is applied on an object of mass 1 kg and it is accelerated by $1\,m/{\sec ^2}$.
Mathematically,
$1N = 1kg\times 1\,m/{\sec ^2}$
$1N = 1000gm\times 100cm/{\sec ^2}$
$1N = {10^5}dyne$
$1N/{m^2} = \frac{{{{10}^5}\,dyne}}{{{{({{10}^2})}^2}\,c{m^2}}} = 10\,dyne/c{m^2}\,$
Given value of pressure is ${10^3}$dyne$/c{m^2}$
$ = {10^3}dyne/c{m^2}$
$ = {10^2}N/{m^2}$
Therefore, the correct option is B.

Note: We can use the elimination method as well. We can use the relations given in each option and try fitting it. If 1 Newton was supposed to be equal to ${10^6}dyne$, then the value of ${10^3}$dyne$/c{m^2}$ would have been equal to $10N/{m^2} $which is wrong because the conversion from newton to dyne is not correct.