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JEE Main 202331 JanuaryEvening Shift
Exam
JEE Main
Year
2023
Date
31 January
Shift
Evening Shift
Subject
Physics
Chapter
Waves and Sound

JEE Main 2023 · 31 January · Evening Shift · Physics · Waves and Sound

For a solid rod, the Young's modulus of elasticity is 3 . 2 × 10 ^...

For a solid rod, the Young's modulus of elasticity is 3.2×1011Nm−23 . 2 \times {10}^{11}N{m}^{- 2} and density is 8×103kgm−38 \times {10}^{3}kg{m}^{- 3}. The velocity of longitudinal wave in the rod will be

Options

  1. A145.75×103ms−1145 . 75 \times {10}^{3}m{s}^{- 1}
  2. B3.65×103ms−13 . 65 \times {10}^{3}m{s}^{- 1}
  3. C18.96×103ms−118 . 96 \times {10}^{3}m{s}^{- 1}
  4. D6.32×103ms−16 . 32 \times {10}^{3}m{s}^{- 1}

Correct answer

D. 6.32×103ms−16 . 32 \times {10}^{3}m{s}^{- 1}

Step-by-step solution

The velocity of longitudinal wave in the rod will be, v=Yρ=3.2×10118×103v = \sqrt{\dfrac{Y}{ρ}} = \sqrt{\dfrac{3 . 2 \times {10}^{11}}{8 \times {10}^{3}}}

=2×10310= 2 \times {10}^{3}\sqrt{10}

≈6.32×103ms−1\approx 6 . 32 \times {10}^{3}m{s}^{- 1}

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