In CGS System, the magnitude of the force is 100 dynes. In another system, where the fundamental physical quantities are kilogram, meter, and minute, find the magnitude of the force is $\dots \times {10}^{-1}$ units.

We have,

 ${\mathrm{n}}_1=100, {\mathrm{M}}_1=\mathrm{g}, {\mathrm{L}}_1=\mathrm{cm}, {\mathrm{T}}_1=\mathrm{s}$ 

and,

 ${\mathrm{M}}_2=\mathrm{kg},{\mathrm{L}}_2=\mathrm{m},{\mathrm{T}}_2=\min$

and, the dimensional formula of forces is $\left[{\mathrm{M}}^1{\mathrm{L}}^1{\mathrm{T}}^{-2}\right]$ where a = 1, b = 1, c = -2.

By substituting these values in the following conversion formula, we have

${\mathrm{n}}_2={\mathrm{n}}_1{\left[\frac{{\mathrm{M}}_1}{{\mathrm{M}}_2}\right]}^{\mathrm{a}}{\left[\frac{{\mathrm{L}}_1}{{\mathrm{L}}_2}\right]}^{\mathrm{b}}{\left[\frac{{\mathrm{T}}_1}{{\mathrm{T}}_2}\right]}^{\mathrm{c}}$

$=100{\left[\frac{\mathrm{g}}{\mathrm{kg}}\right]}^1{\left[\frac{\mathrm{cm}}{\mathrm{m}}\right]}^1{\left[\frac{\mathrm{s}}{\min }\right]}^{-2}$

$=100{\left[\frac{\mathrm{g}}{{10}^3\mathrm{g}}\right]}^1{\left[\frac{\mathrm{cm}}{{10}^2\mathrm{cm}}\right]}^1{\left[\frac{\mathrm{s}}{60\mathrm{s}}\right]}^{-2}=3.6$