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