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A longitudinal wave is observed travelling through a metallic wire at a speed of 5000 m s ⁻¹ . If the density of the metal is 8000 kg m ⁻³ , the Young's modulus of the material of the wire is

Options

  1. A4.0 10⁷ N m ⁻²
  2. B2.0 10¹¹ N m ⁻²
  3. C3.125 10³ N m ⁻²
  4. D6.32 10³ N m ⁻²

Correct answer

B. 2.0 10¹¹ N m ⁻²

Step-by-step solution

The speed of a longitudinal wave in a solid medium is given by the formula: v = Y where Y is the Young's modulus and is the density of the material. Squaring both sides to solve for Y , we get: Y = v² Substituting the given values: Y = (5000)² 8000 Y = (25 10⁶) (8 10³) Y = 200 10⁹ = 2.0 10¹¹ N m ⁻² Answer: 2.0 10¹¹ N m ⁻²

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