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For a solid rod of Young's modulus 3.2×10¹¹ N m⁻² and density 8×10³ kg m⁻³, the velocity of a longitudinal wave in the rod is
Asked in JEE Main 31st Jan 2nd Shift 2023 · Longitudinal wave in a solid
- (1) 3.65×10³ m s⁻¹
- (2) 18.96×10³ m s⁻¹
- (3) 145.75×10³ m s⁻¹
- (4) 6.32×10³ m s⁻¹
Answer: (4) 6.32×10³ m s⁻¹
Step-by-step solution
v=√Y/ρ=√(3.2×10¹¹)/(8×10³)=√4×10⁷.
v=6.32×10³ m s⁻¹.
Why the other options are wrong
- (1) Halves the correct value.
- (2) Loses a power of ten inside the root.
- (3) Omits the square root on the power of ten.
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