To solve this problem, we will use the principle of a potentiometer, which states that the potential difference across a length of wire is directly proportional to the length of the wire.$\\$Given:$\\$• EMF of the first cell $E_1 = 1.5$ V, balance point at $L_1 = 36$ cm.$\\$• EMF of the second cell $E_2 = 2.5$ V, balance point at $L_2$ cm (to be found).$\\$According to the potentiometer principle:$\\ \frac{E_1}{E_2} = \frac{L_1}{L_2} \\$Substitute the known values:$\\ \frac{1.5}{2.5} = \frac{36}{L_2} \\$Simplify the left side:$\\ \frac{3}{5} = \frac{36}{L_2} \\$Cross-multiply to solve for $L_2: \\ 3 \cdot L_2 = 5 \cdot 36 \\ L_2 = \frac{5 \cdot 36}{3} \\ L_2 = \frac{180}{3} \\ L_2 = 60$ cm$\\$Therefore, the balance point occurs at $60$ cm, which corresponds to Option 1.