Question

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.

Answer 1

We have $n_1=100,M_1=g,L_1=cm,T_1=s$ and $M_2=kg,L_2=m,T_2=min,$

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

By substituting these values in the following conversion formula, we have
$n_2=n_1{\left[\frac{M_1}{M_2}\right]}^a{\left[\frac{L_1}{L_2}\right]}^b{\left[\frac{T_1}{T_2}\right]}^c$

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

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