Question

The speed of a transverse wave passing through a string of length 50 cm and mass 10 g is 60 ms^–1. The area of cross-section of the wire is 2.0 mm² and its Young’s modulus is 1.2 × 10¹¹ Nm^–2. The extension of the wire over its natural length due to its tension will be x × 10^–5 m. The value of x is _____.

Answer 1

Correct Answer: 15

\(v=\sqrt{\frac{T}{μ}}\)
So,\( T=60^2×\frac{10×10^{−3}}{0.5}\)
=72 N
\(Δℓ=\frac{Tℓ}{YA}=\frac{72×0.5}{1.2×10^{−11}×2×10^{−6}}\)
=15×10⁻⁵ m
Given that, the extension of the wire over its natural length due to its tension is x × 10^–5 m.
On comparing, x = 15
So, the answer is 15.