Question

Convert Newton into dyne.

Answer 1

The Newton is the SI unit of force and has dimensional formula [$M^1{L}^1{T}^{-2}$], i.e., a = $1$, b = $1$, c = $-2$
So $1$N = $1kgm{s}^{-2}$

SI system	CGS system
$M_1=1$kg	$M_2=1$kg
$L_1=1m$	$L_2=1cm$
$T_1=1$ s	$T_2=1$ s

By using $n_2=n_1{\left[\frac{M_1}{M_2}\right]}^a{\left[\frac{L_1}{L_2}\right]}^b{\left[\frac{T_1}{T_2}\right]}^c$
$=1{\left[\frac{kg}{g}\right]}^1{\left[\frac{m}{cm}\right]}^1{\left[\frac{s}{s}\right]}^{-2}$
$=1{\left[\frac{{10}^{3}g}{g}\right]}^1{\left[\frac{{10}^{2}cm}{cm}\right]}^1{\left[\frac{s}{s}\right]}^{-2}={10}^5$
$\therefore$ 1 N $={10}^{5}Dyne$