Question

To find the convergence factor between the units of same physical quantities in two different system

Answer 1

To find the conversion factor b/w the units of force-

i.e newton in si system to dyne is cgs system-

in x dyne

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

$\left[{L_1}^1{M_1}^1{T_1}^{-2}\right]=X\left[{L_2}^1{M_2}^1{T_2}^{-2}\right]$

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

WHERE suffix I indicates si system and suffix 2 indicates c.g.s – system

In S.I. system L,M and T are expressed in m, kg,scgs system, L,M and T are expressed in m,g,s

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

$=\left({10}^2\right)\left({10}^3\right){\left(1\right)}^{-2}$

$x={10}^5$

$1N={10}^{5}dyne$