Two wires are made of the same material and have the same volume. However wire 1 has cross-sectional area A and wire-2 has cross-sectional area 3A . I - Physics MCQ AIEEE 2009 2026 | ExamTest.live

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Two wires are made of the same material and have the same volume. However wire 1 has cross-sectional 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 much force is needed to stretch wire 2 by the same amount?

Solution & Step-by-step Explanation

Young's Modulus Y = \frac{F / A}{Δ L / L} ⟹ F = Y A \frac{Δ L}{L} .Since volume V = A L is constant: L = \frac{V}{A} .Substituting L : F = Y A \frac{Δ x}{V / A} = \frac{Y A ^{2} Δ x}{V} .For the same material (Y), same volume (V), and same extension (Δ x): F \propto A^{2} . \frac{F _{2}}{F _{1}} = (\frac{A _{2}}{A _{1}})^{2} = (\frac{3 A}{A})^{2} = 9 . F_{2} = 9 F .

Try it yourself before checking the explanation above.

Two wires are made of the same material and have the same volume. However wire 1 has cross-sectional 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 much force is needed to stretch wire 2 by the same amount?

F

4 F

6 F

9 F

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