Two wires are made of the same material and have the same volume. However wire 1 has crosssectional area A and wire 2 has cross-sectional area 3 A . If the length of wire 1 increases by Δ x on applying force F , how

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Correct answer: C. 9 F

Two wires are made of the same material and have the same volume. However wire 1 has crosssectional area A and wire 2

As shown in the figure, the wires will have the same Young's modulus (same material) and the length of the wire of area of crosssection

3 A

will be

\ell / 3

(same volume as wire 1 ). For wire

1, \quad Y=\frac{F / A}{\Delta x / \ell}

For wire

2, Y=\frac{F^{\prime} / 3 A}{\Delta x /(\ell / 3)}

From (i) and (ii)

, \frac{F}{A} \times \frac{\ell}{\Delta x}=\frac{F^{\prime}}{3 A} \times \frac{\ell}{3 \Delta x}\Rightarrow F^{\prime}=9 F

Two wires are made of the same material and have the same volume....

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