of the wire $(\mathrm{m}=\mathrm{M} / \mathrm{L})$

Let $\left.A \propto L^{a} F^{b} m^{c} \quad \text { ……….. } \quad \text { (Equation } 1\right)$

Writing the dimensions of each in the above equation, we get

$\left[\mathrm{M}^{0} \mathrm{L}^{0} \mathrm{T}^{-1}\right]=\mathrm{L}^{\mathrm{a}}\left[\mathrm{M}^{1} \mathrm{L}^{1} \mathrm{T}^{-2}\right]^{\mathrm{b}}\left[\mathrm{M}^{0} \mathrm{L}^{-1}\right]^{\mathrm{C}}$

$=M^{b+c} L^{a+b-c} T^{-2 b}$

Here, $b+c=0$

$a+b-c=0 \text { and }$

$-2 b=-1$

On solving, we get

$a=-1, b=1 / 2$ and $c=-1 / 2$

Substituting these values in equation $(1),$ we get

$A=k L^{-1} F^{1 / 2} m^{-1 / 2}$

$=k \frac{1}{L} \sqrt{\frac{F}{m}}$

or $A=k \frac{1}{L} \sqrt{\frac{F}{(M / L)}}$

or $A=k \sqrt{\frac{F}{M L}}$

Experimentally $\mathrm{k}=1 / 2$ $\therefore A=\frac{1}{2} \sqrt{\frac{F}{M L}}$