${[F]=k[x]^{3}=\left[ MLT ^{-2}\right]=k\left[ I ^{3}\right]}$

$\Rightarrow \quad\lfloor k]=\left[ ML ^{-2} T ^{-2}\right]$

$\text { Since, } \quad T \propto[ M ]^{a}[ A ]^{b}[k]^{c}$

$\Rightarrow \quad\left[ T ^{\prime}\right]=[ M ]^{a}\left[ L ^{b}\left[ ML ^{-2} T ^{-2}\right]^{c}\right.$

$\text { Comparing powers, we get }$

$a+c=0$ ................$(i)$

$b-2 c=0$ ................$(ii)$

$-2 c=1$ ................$(iii)$

Solving Eqs. $(i), (ii)$ and $(iii)$, we get

$a=\frac{1}{2}, b=-1, c=-\frac{1}{2}$

$\therefore T \propto \frac{1}{L} \sqrt{\frac{M}{k}} \Rightarrow T \propto \frac{1}{L}$

$\therefore \quad \frac{T_{1}-A_{2}-2 A}{T_{2} \frac{A_{1}}{A}} \quad(\because \text { Here } L=A)$ 

$\Rightarrow$ $\frac{T_{2}-T_{1}-T}{2}$ $\left(\because T_{1}=T\right)$