Two wires are made of the same material and have the same volume. The first wire has cross-sectional area A and the second wire has cross-sectional ar - Physics MCQ NEET (UG) 2018 2026 | ExamTest.live

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Two wires are made of the same material and have the same volume. The first wire has cross-sectional area A and the second wire has cross-sectional area 3 A . If the length of the first wire is increased by Δ l on applying a force F, how much force is needed to stretch the second wire by the same amount?

Solution & Step-by-step Explanation

1. Young's Modulus Y = \frac{F / A}{Δ l / l} ⟹ F = \frac{Y A Δ l}{l} .2. Since Volume V = A \times l is constant, l = \frac{V}{A} .3. Substituting l : F = \frac{Y A Δ l}{V / A} = \frac{Y A ^{2} Δ l}{V} .4. For the same material (Y), same volume (V), and same extension (Δ l): F \propto A^{2} 5. For the second wire, area is 3 A, so: F^{'} \propto (3 A)^{2} = 9 A^{2} = 9 F

Try it yourself before checking the explanation above.

Two wires are made of the same material and have the same volume. The first wire has cross-sectional area A and the second wire has cross-sectional area 3 A . If the length of the first wire is increased by Δ l on applying a force F, how much force is needed to stretch the second wire by the same amount?

4 F

6 F

9 F

F

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