The speed of a transverse wave going on a wire having length 50 cm and mass 5 g is 80 m/s. The area of cross section of wire is 1.0 mm² and its Young’s modulus is 8 × 10¹¹ N/m². Find the extension (in ×10⁻² mm) of the wire over its natural length.
Physics · Mixed Chapter
JEE Mains

Question

The speed of a transverse wave going on a wire having length 50 cm and mass 5 g is 80 m/s. The area of cross section of wire is 1.0 mm² and its Young’s modulus is 8 × 10¹¹ N/m². Find the extension (in ×10⁻² mm) of the wire over its natural length.

Physics · Mixed Chapter

G1 Physics · Accepted Answer

Step 1: Linear density μ=m/L=0.005/0.5=0.01 kg m⁻¹. A string wave has v=√(F/μ), so tension F=μv²=0.01×80²=64 N. Step 2: Extension ΔL=FL/(AY) with L=0.5 m, A=10⁻⁶ m² and Y=8×10¹¹ N m⁻². Step 3: ΔL=(64×0.5)/(10⁻⁶×8×10¹¹)=4×10⁻⁵ m=0.04 mm. Step 4: In units of 10⁻² mm this is 4, so answer 4.