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JEE Main 2019 (8 Apr, Shift 2) · Young's Modulus & Elongation

Young's Modulus & Elongation question from JEE Main 2019 (8 Apr, Shift 2)

Q26JEE Main 2019 · 8 APR · SHIFT 2Medium

Young's Modulus & Elongation

Young's moduli of two wires A and B are in the ratio 7: 4. Wire A is 2 m long and has radius R. Wire B is 1.5 m long and has radius 2 mm. If the two wires stretch by the same length for a given load, then the value of R is close to :-

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Answer: (a)

  1. Same load and extension: Y=FLπr2Δl∝Lr2Y = \frac{FL}{\pi r^2 \Delta l} \propto \frac{L}{r^2}
  2. 74=2/R21.5/(2 mm)2=81.5R2\frac{7}{4} = \frac{2/R^2}{1.5/(2\text{ mm})^2} = \frac{8}{1.5R^2}
  3. R2=3210.5≈3.05 mm2⇒R≈1.75 mmR^2 = \frac{32}{10.5} \approx 3.05\text{ mm}^2 \Rightarrow R \approx 1.75\text{ mm}
  4. So the answer is (a) 1.7 mm.
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