Potentiometer balancing requires total wire length or resistance per unit length

Steps:

• The balancing condition requires the potential difference across the 0.40 m portion to equal the solar cell's e.m.f. of 1.5 V.
• Wire resistance is 5.0 Ω total, but total length L is not given, so resistance of 0.40 m portion = 5 × (0.40 / L) Ω is unknown.
• Primary current I = 2.0 / (R + 5.0 + 0.50) = 2.0 / (R + 5.5), so PD across portion = I × [5 × (0.40 / L)] = 1.5 V.
• Equation has two unknowns (R and L), cannot solve for R.

Not enough information.

Final answer: Not enough information.