A uniform wire of length 50 cm, mass 5.0 g and cross-sectional area 1.0 mm² carries transverse waves at 80 m s⁻¹. Young modulus is 16 × 10⁹ N m⁻². Find extension of the wire (mm).
Physics · Mixed Chapter
JEE Main Practice

Question

A uniform wire of length 50 cm, mass 5.0 g and cross-sectional area 1.0 mm² carries transverse waves at 80 m s⁻¹. Young modulus is 16 × 10⁹ N m⁻². Find extension of the wire (mm).

G1 Physics · Accepted Answer

Step 1 — Mass per unit length μ = 0.005/0.5 = 0.01 kg m⁻¹. Step 2 — From wave speed v = √(F/μ), tension F = μv² = 0.01 × 80² = 64 N. Step 3 — Longitudinal strain ε = F/(YA), and elongation ΔL = FL/(YA). Step 4 — ΔL = (64 × 0.50)/(16 × 10⁹ × 10⁻⁶) = 2 × 10⁻³ m = 2 mm.