Question

Using Dimensional analysis convert newton into dyne.

Answer 1

the dimensional formula of Force $F=\left[M^1{L}^1{T}^{-2}\right]$

So $a=1,b=1,c=-2$

Now because Newton is in m.k.s system, we have

$M_1=1kg$

$L_1=1m$

$T_1=1s$

$M_2=1g$

$L_2=1cm$

$T_2=1s$

$n_1=1Newton$

$n_2=?$

Using the formula

$n_2=n_1\left[M1/M2{]}^a\right[L1/L2{]}^b[T1/T2{]}^c$

$n_2=1\left[1kg/1g{]}^1\right[1m/1cm{]}^1[1s/1s{]}^{-2}$

$n_2=1\left[1000g/1g{]}^1\right[100cm/1cm{]}^{1\times 1}$

$n_2=1000\times 100=100000={10}^{5}dynes$