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JEE Main 202628 JanuaryMorning Shift
Exam
JEE Main
Year
2026
Date
28 January
Shift
Morning Shift
Subject
Physics
Chapter
Mechanical Properties of Solids

JEE Main 2026 · 28 January · Morning Shift · Physics · Mechanical Properties of Solids

Two wires A and B made of different materials of lengths 6.0 cm and...

Two wires AA and BB made of different materials of lengths 6.0 cm and 5.4 cm, respectively and area of cross sections 3.0×10−5 m23.0 \times 10^{-5} \mathrm{~m}^{2} and 4.5×10−5 m24.5 \times 10^{-5} \mathrm{~m}^{2}, respectively are stretched by the same magnitude under a given load. The ratio of the Young's modulus of AA to that of BB is x:3x: 3. The value of xx is ____\_\_\_\_.

Options

  1. A2
  2. B1
  3. C4
  4. D5

Correct answer

D. 5

Step-by-step solution

Young's modulus: Y=σϵ=F/AΔL/LY = \frac{\sigma}{\epsilon} = \frac{F/A}{\Delta L/L}.
When the same force is applied and both wires stretch by the same extension ΔL\Delta L, the ratio of Young's moduli is:
YAYB=F/AAΔL/LA×ΔL/LBF/AB=ABAA×LALB\frac{Y_A}{Y_B} = \frac{F/A_A}{\Delta L/L_A} \times \frac{\Delta L/L_B}{F/A_B} = \frac{A_B}{A_A} \times \frac{L_A}{L_B}
=4.5×10−53.0×10−5×6.05.4=1.5×109=53=\frac{4.5 \times 10^{-5}}{3.0 \times 10^{-5}} \times \frac{6.0}{5.4} = 1.5 \times \frac{10}{9} = \frac{5}{3}.
Therefore x:3=5:3x : 3 = 5 : 3, giving x=5x = 5.
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