JEE Main 2026 — Jan 28, Shift 2 — Physics solution

JEE Main2026Jan 28, Shift 2Physics

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.

A
399
B
398
C
402
D
401

Solution

$v = \frac{Y}{ρ}$ . Taking logarithmic differentials: $\frac{Δ v}{v} \times 100 = \frac{1}{2} (\frac{Δ Y}{Y} \times 100) - \frac{1}{2} (\frac{Δ ρ}{ρ} \times 100)$ .

$= \frac{1}{2} (1) - \frac{1}{2} (0.5) = 0.25%$ .

$Δ v = 0.0025 \times 400 = 1$ m/s. New speed $\approx 401$ m/s.

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