Question

Derive the relationship between S. I. unit and C. G. S. unit of force​

Answer 1

Answer:

Relation is 1N=100000dyne

Answer 2

Since the dimension of the force,

• $\displaystyle\sf {[F]=M\ L\ T^{-2}}$

the unit of force in SI unit is,

$\displaystyle\longrightarrow\sf {1\ N=1\ kg\ m\ s^{-2}\quad\quad\dots (1)}$

But,

• $\displaystyle\sf {1\ kg=10^3\ g}$

• $\displaystyle\sf {1\ m=10^2\ cm}$

Then (1) becomes,

$\displaystyle\longrightarrow\sf {1\ N=10^3\times 10^2\ g\ cm\ s^{-2}}$

$\displaystyle\longrightarrow\sf {\underline {\underline {1\ N=10^5\ g\ cm\ s^{-2}}}}$

Or,

$\displaystyle\longrightarrow\sf {\underline {\underline {1\ kg\ m\ s^{-2}=10^5\ g\ cm\ s^{-2}}}}$

This is the relation between the SI and CGS units of force.

Well, $\displaystyle\sf {1\ g\ cm\ s^{-2}}$ is known by the name dyne, and hence,

$\displaystyle\longrightarrow\sf {\underline {\underline {1\ Newton=10^5\ dyne}}}$