a
First case \(\frac{2}{40}=\frac{X}{60} \Rightarrow X=3 \Omega\)

In second case \(X^{\prime}=\frac{2 \times 3}{2+3}=1.2 \Omega\)

\(\frac{2}{\ell}=\frac{1.2}{100-\ell}\)

\(200-2 \ell=1.2 \ell\)

\(\ell=\frac{200}{3.2}=62 . \mathrm{bm}\)

Balance length changes by \(22.5 \mathrm{~cm}\)