Question

One dyne is equal to
a). ${9^5}$ newton
b). ${10^6}$ newton
c). ${10^{ - 6}}$ newton
d). ${10^{-5}}$ newton

Answer 1

Hint: In this question we start with the definition of newton that is the SI unit of force and its unit is \[Kg.m/{s^2}\] whereas dyne is the CGS unit of force and its unit is \[g.cm/{s^2}\] . Then we convert newton to dyne using the expression \[1N = 1Kg \times 1m/{s^2} = 1000g \times 100cm/{s^2}{\text{ }}\] .

Complete step-by-step solution -
We know that both Dyne and Newton are the units denoting force but in two different systems.
The difference between these two is that under the International System of Units (SI Units) we use Newton as the derived unit of force whereas, under the Centimeter-Gram-Second (CGS) units system dyne is used as a derived unit of force
It is very important to know the relation between dyne and newton solving numerical.
The definition of Dyne is the force needed for accelerating a mass of one gram with an acceleration of one centimeter per second squared that is 1 \[cm/{s^2}\] . Therefore its unit is given as \[g.cm/{s^2}\]
However, the definition Newton is the force needed for accelerating a mass of one kilogram with an acceleration of one meter per second squared which is 1 \[m/{s^2}\]. Therefore its unit is given as \[Kg.m/{s^2}\]
Now to convert newton to Dyne, we start with the unit of 1 Newton that is.
\[1N = Kg.m/{s^2} = 1Kg \times 1m/{s^2}\]
\[ \Rightarrow 1000g \times 100cm/{s^2}{\text{ }}\]
\[ \Rightarrow 1000 \times 100g \times cm/{s^2}{\text{ }}\]
\[ \Rightarrow {10^5}g.cm/{s^2}{\text{ }}\]
Hence, we get the final result which is giving us the relation to convert newton to dyne that is
\[1N = {10^5}g.cm/{s^2}{\text{ }}\]
Now to convert dyne to newton we can write it as
\[1 \text{dyne} = {10^{ - 5}}Kg.m/{s^2}{\text{ }}\]
So, \[1 \text{dyne} = {10^{ - 5}}\text{N} \]
Dyne is CGS unit of force so its unit as we have seen is mass multiplied by acceleration therefore, its dimensional formula is also the same as the force that is $\left[ {{M^1}{L^1}{T^{ - 2}}} \right]$.

Note: For these types of questions we need to have a clear understanding of both the SI and CGS units of some well-known terms like force, pressure, acceleration, velocity, mass, etc. We also need to know how to convert the SI unit to CGS and vice versa.