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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

Asked in JEE Main 31st Jan 2nd Shift 2023 · Elongation under a load

• (1) 1:4
• (2) 1:1
• (3) 1:10
• (4) 1:2

Step-by-step solution

Why the other options are wrong

• (1) comes from no consistent slip lands here; the numbers are chosen so that L/A is 2×10⁵ m⁻¹ for both wires, so even inverting the ratio still returns 1:1. A factor of 4 can only come from inventing one.
• (3) comes from filler in the same way; (L_A)/(L_B)=5/6 and (A_B)/(A_A)=6/5 are the only ratios in the data, and no product of them is 1/(10).
• (4) comes from stopping at one of the two ratios and rounding: (2.5)/(3.0)≈0.83 read loosely as 'about a half', with the length ratio never brought in to cancel it.

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