Question

$1Pascal$=_______ $dyne\,c{m^{ - 2}}$
A. $10$
B. $\dfrac{1}{{10}}$
C. $100$
D. $1000$

Answer 1

A unit of measurement is a fixed magnitude of a quantity that is used as a standard for measuring other quantities of the same kind. It is specified and recognised by law or convention. A multiple of the unit of measurement may be used to express some other quantity of that kind.

Complete step-by-step solution:
Dyne: "The force needed to accelerate a mass of one gram at a rate of one centimetre per second squared," says the dyne. The dyne can also be described as "that force that, when acting for one second, causes a change in velocity of one centimetre per second in a mass of one gram."
Pascal: Internal strain, stress, Young's modulus, and ultimate tensile strength are all measured in pascals, a SI-derived unit of pressure. The unit is one newton per square foot, which in the CGS scheme is equivalent to $10{\text{ }}barye$ . Blaise Pascal was the inspiration for the name.
Now, coming to the question;
$1N = {10^5}Dyne$
$1{m^2} = {10^4}c{m^2}$
$N/{m^2} = 10Dyne/c{m^2}$
$1{\text{ }}Pa{\text{ }} = {\text{ }}10{\text{ }}dyn/c{m^2}.$ $\left[ {\because N/{m^2} = 1Pa} \right]$
So, the correct option is (A) $10$.

Note: A conversion factor is a formula that expresses the relationship between units and is used to adjust the units of a measured quantity without altering its value. When the numerator and denominator have the same value expressed in different units, the conversion ratio (or unit factor) is always one (1).