Convert 1N into dyne using dimensional analysis.

Explanation

The newton is unit of force in SI and dyne in CGS system
Dimensional formula for force `=[MLT^(-2)]`

Using `n_(2)=n_(1)[(M_(1))/(M_(2))]^(a)[(L_(1))/(L_(2))]^(b)[(T_(1))/(T_(2))]^(c )`, we get
Here `a=1`, `b=1` and `c=-2` therefore
`n_(2)=1[(1kg)/(1g)]^(1)[(1m)/(1cm)]^(1)[(1s)/(1s)]^(-2)=[(10^(3)g)/(1g)][(100cm)/(1cm)][(1s)/(1s)]^(-2)=10^(5)`
Using, `n_(1)u_(1)=n_(2)u_(2)`, we get 1 newton `=10^(5)` dyne.