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JEE Main 2026 (28 Jan, Shift 2) · Errors in Measurement

Errors in Measurement question from JEE Main 2026 (28 Jan, Shift 2)

Q31JEE Main 2026 · 28 JAN · SHIFT 2Medium

Errors in Measurement

The speed of a longitudinal wave in a metallic bar is 400 m/s. If the density and Young's modulus of the bar material are increased by 0.5% and 1%, respectively then the speed of the wave is changed approximately to ______ m/s.

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Answer: (c)

  1. Longitudinal wave in a bar: v=Y/ρv = \sqrt{Y/\rho}.
  2. For small changes: Δvv=12(ΔYY−Δρρ)=12(1%−0.5%)=0.25%\frac{\Delta v}{v} = \frac{1}{2}\left(\frac{\Delta Y}{Y} - \frac{\Delta \rho}{\rho}\right) = \frac{1}{2}(1\% - 0.5\%) = 0.25\%
  3. Δv=0.0025×400=1 m/s\Delta v = 0.0025 \times 400 = 1\text{ m/s}, so v≈401 m/sv \approx 401\text{ m/s}
  4. So the answer is (c) 401.
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