Question

Convert 1 dyne into newton.

Answer 1

Step 1 : Deriving CGS unit of force.

$$\begin{gathered} Force=mass\left(m\right)\times acceleration \\ CGSunitofmass=grams\left(g\right) \\ CGSunitofacceleration=\raisebox{1ex}{$cm$}\!\left/ \!\raisebox{-1ex}{$s^2$}\right. \\ CGSunitofForce=g\times \raisebox{1ex}{$cm$}\!\left/ \!\raisebox{-1ex}{$s^2$}\right. \\ =g\raisebox{1ex}{$cm$}\!\left/ \!\raisebox{-1ex}{$s^2$}\right. \\ =dyne \end{gathered}$$

Step 2 :Deriving SI unit of force

$$\begin{gathered} Force=mass\left(m\right)\times accelaration \\ SIunitofmass=ki\log ram\left(kg\right) \\ SIunitofacceleration=\raisebox{1ex}{$m$}\!\left/ \!\raisebox{-1ex}{$s^2$}\right. \\ SIunitofForce=kg\times \raisebox{1ex}{$m$}\!\left/ \!\raisebox{-1ex}{$s^2$}\right. \\ =kg\raisebox{1ex}{$m$}\!\left/ \!\raisebox{-1ex}{$s^2$}\right. \\ =newton \end{gathered}$$

Step 3 :Conversion of 1 dyne into newton

$$\begin{gathered} 1dyne=1g\times 1\raisebox{1ex}{$cm$}\!\left/ \!\raisebox{-1ex}{$s^2$}\right. \\ 1gram={10}^{-3}kg \\ 1cm={10}^{-2}m \\ 1dyne={10}^{-3}kg\times {10}^{-2}\raisebox{1ex}{$m$}\!\left/ \!\raisebox{-1ex}{$s^2$}\right. \\ ={10}^{-5}kg\raisebox{1ex}{$m$}\!\left/ \!\raisebox{-1ex}{$s^2$}\right. \\ ={10}^{-5}newton \end{gathered}$$

Hence,$1dyne={10}^{-5}newton.$