Resistance scales with length squared for same-mass wires

Steps:

• Resistance R = ρL/A; same material means same ρ.
• Same mass means same volume V = L × A, so A = V/L.
• Second wire L₂ = 3L₁, so A₂ = V/(3L₁) = A₁/3.
• Thus R₂ = ρ(3L₁)/(A₁/3) = 9(ρL₁/A₁) = 9R₁ = 9×30Ω = 270Ω.

Why D is correct:

• Ohm's law: R ∝ L/A; constant volume makes A ∝ 1/L, so R ∝ L².

Why the others are wrong:

• A: Assumes resistance decreases, ignoring area reduction.
• B: Assumes resistance unchanged, ignoring length and area changes.
• C: Assumes resistance triples with length, ignoring area halving effect.

Final answer: D