Resistance formula for wires of same material

Steps:

• Resistance R = ρL/A; ρ is constant, so R₂/R₁ = (L₂/L₁) × (A₁/A₂).
• L₂/L₁ = 2.0 / 0.50 = 4; A₁/A₂ = 1.0×10⁻² / 5.0×10⁻² = 0.2.
• R₂/R₁ = 4 × 0.2 = 0.8.
• R₂ = 0.8 × 0.75 Ω = 0.60 Ω.

Why A is correct:

• Matches R = ρL/A, where ratio of lengths over areas gives exact value.

Why the others are wrong:

• B: Underestimates ratio by halving length effect.
• C: Ignores area increase, just quadruples resistance.
• D: Reverses area effect, treating it as decreasing resistance.

Final answer: A