Question

Using dimensions, show that $1newton={10}^{5}dyne$

Answer 1

Let $1$ $newton$ $=n$ $dynes$

$n=\frac{M_1{L}_1{t_1}^{-2}}{M_2{L}_2{t_2}^{-2}}=\frac{M_1}{M_2}\times \frac{L_1}{L_2}\times \frac{{t_1}^{-2}}{{t_2}^{-2}}$

$=\frac{Rg}{gm}\times \frac{m}{cm}\times {\left(\frac{s}{s}\right)}^{-2}$

$=\frac{{10}^{3}gm}{gm}\times \frac{{10}^{2}cm}{cm}\times s^0$

$={10}^3{10}^2={10}^5$

$\therefore 1newton={10}^{5}dyne.$

Hence,

we get,

$1newton={10}^{5}dyne.$