Question

Using the dimensional method derive the relation between the units of force in the SI and CGS system.

Answer 1

Let $1$ newton(SI) = $x$ dyne(CGS)

Dimensions of forces are $\left[L^1{M}^1{T}^{-2}\right]$

$\therefore \left[L_1^1{M}_1^1{T}_1^{-2}\right]=x\left[L_2^1{M}_2^1{T}_2^{-2}\right]$

$\therefore x=\left(\frac{L_1}{L_2}{)}^1\right(\frac{M_1}{M_2}{)}^1(\frac{T_1}{T_2}{)}^{-2}$

$=\left(\frac{m}{cm}{)}^1\right(\frac{kg}{g}{)}^1(\frac{s}{s}{)}^{-2}$

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

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