For a solid rod, the Young's modulus of elasticity is 3.2 × 10¹¹ N m⁻² and density is 8 × 10³ kg m⁻³. The velocity of longitudinal wave in the rod will be. (a) 3.65 × 10³ m s⁻¹ (b) 6.32 × 10³ m s⁻¹ (c) 18.96 × 10³ m s⁻¹ (d) 145.75 × 10³ m s⁻¹

Answer: (b). Speed of longitudinal wave in a rod: v = √(Y/ρ) v = √3.2 × 10¹¹8 × 10³ = √4 × 10⁷ = 6.32 × 10³ m s⁻¹ So the answer is (b).

For a solid rod, the Young's modulus of elasticity is 3.2 × 10¹¹ N… | JEE Main 2023 (31 Jan, Shift 2)

Q10JEE Main 2023 · 31 JAN · SHIFT 2Easy

Young's Modulus & Elongation

For a solid rod, the Young's modulus of elasticity is $3.2 \times 10^{11}\text{ N m}^{-2}$ and density is $8 \times 10^{3}\text{ kg m}^{-3}$ . The velocity of longitudinal wave in the rod will be.

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Answer: (b)

Speed of longitudinal wave in a rod: $v = \sqrt{\frac{Y}{\rho}}$
$v = \sqrt{\frac{3.2 \times 10^{11}}{8 \times 10^{3}}} = \sqrt{4 \times 10^{7}} = 6.32 \times 10^{3}\ \text{m s}^{-1}$
So the answer is (b).

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