Two wires A and B are made of same material having ratio of lengths (LA)/(LB) = 1/3 and their diameters ratio (dA)/(dB) = 2. If both the wires are stretched using same force, what would be the ratio of their respective elongations? (a) 3: 4 (b) 1: 12 (c) 1: 3 (d) 1: 6

Answer: (b). Same material and force: Δ L ∝ L/d² (Δ LA)/(Δ LB) = (LA)/(LB) × ((dB)/(dA))² = 1/3 × 1/4 = 1/12 So the answer is (b) 1: 12.

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Young's Modulus & Elongation

Two wires A and B are made of same material having ratio of lengths $\frac{L_A}{L_B} = \frac{1}{3}$ and their diameters ratio $\frac{d_A}{d_B} = 2$ . If both the wires are stretched using same force, what would be the ratio of their respective elongations?

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Answer: (b)

Same material and force: $\Delta L \propto \frac{L}{d^2}$
$\frac{\Delta L_A}{\Delta L_B} = \frac{L_A}{L_B} \times \left(\frac{d_B}{d_A}\right)^2 = \frac{1}{3} \times \frac{1}{4} = \frac{1}{12}$
So the answer is (b) $1 : 12$ .

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