Under the same load, wire A having length 5.0 m and cross section 2.5 × 10⁻⁵ m² stretches uniformly by the same amount as another wire B of length 6.0 m and a cross section of 3.0 × 10⁻⁵ m² stretches. The ratio of the Young's modulus of wire A to that of wire B will be: (a) 1: 2 (b) 1: 4 (c) 1: 1 (d) 1: 10

Answer: (c). Y = (FL)/(AΔ l); same F and same Δ l, so Y ∝ L/A. (YA)/(YB) = 5.0/2.5 × 10⁻⁵6.0/3.0 × 10⁻⁵ = 2 × 10⁵2 × 10⁵ = 1 So the answer is (c) 1: 1.

Under the same load, wire A having length 5.0 m and cross section 2.5… | JEE Main 2023 (31 Jan, Shift 2)

Q16JEE Main 2023 · 31 JAN · SHIFT 2Easy

Young's Modulus & Elongation

Under the same load, wire A having length $5.0\text{ m}$ and cross section $2.5 \times 10^{-5}\text{ m}^2$ stretches uniformly by the same amount as another wire B of length $6.0\text{ m}$ and a cross section of $3.0 \times 10^{-5}\text{ m}^2$ stretches. The ratio of the Young's modulus of wire A to that of wire $B$ will be:

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Answer: (c)

$Y = \frac{FL}{A\Delta l}$ ; same $F$ and same $\Delta l$ , so $Y \propto \frac{L}{A}$ .
$\frac{Y_A}{Y_B} = \frac{5.0/2.5 \times 10^{-5}}{6.0/3.0 \times 10^{-5}} = \frac{2 \times 10^{5}}{2 \times 10^{5}} = 1$
So the answer is (c) $1 : 1$ .

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