Hooke's Law: Extension δ = (F L)/(A Y)

Steps:

• Hooke's law gives extension δ = (F L)/(A Y), with F as tension, L as length, A as cross-sectional area, Y as Young's modulus.
• Both wires have same material (Y) and length (L).
• Wire Y has twice the diameter of X, so area A_Y = 4 A_X (since A ∝ diameter²).
• Wire Y has twice the tension of X, so F_Y = 2 F_X.
• Thus, δ_Y = (2 F_X L)/(4 A_X Y) = (1/2) (F_X L)/(A_X Y) = e/2.

Why B is correct:

• Extension halves because tension doubles but area quadruples, per δ ∝ F/A in Hooke's law.

Why the others are wrong:

• A ignores tension increase, underestimating extension.
• C assumes factors cancel evenly, but area effect dominates.
• D overestimates by ignoring area increase.

Final answer: B