Question
Derive a relation between the $S.I.$ and $C.G.S$. unit of force.
✓
Answer
We have Force = Mass × Acceleration
$\therefore \frac{\text { S.I. unit of force }}{\text { C.G.S unit of force }}=\frac{ kg \times ms ^{-2}}{ g \times cm s ^{-2}}=\left(\frac{ kg }{ g }\right)\left(\frac{ m }{ cm }\right)=10^3 \times 10^2=10^5$
$\therefore$ S.I. unit of force (Newton) $= 10^5 C.G.S$. unit of force (dyne)
Or $1$ Newton $= 10^5$dyne.
$\therefore \frac{\text { S.I. unit of force }}{\text { C.G.S unit of force }}=\frac{ kg \times ms ^{-2}}{ g \times cm s ^{-2}}=\left(\frac{ kg }{ g }\right)\left(\frac{ m }{ cm }\right)=10^3 \times 10^2=10^5$
$\therefore$ S.I. unit of force (Newton) $= 10^5 C.G.S$. unit of force (dyne)
Or $1$ Newton $= 10^5$dyne.
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