Q 11-14-101JEE MainJEE Main 2020 (7 Jan, Shift 1)Medium
The speed of a transverse wave on a straight wire (mass $6.0$ g, length $60$ cm and area of cross-section $1.0\ \text{mm}^2$) is $90\ \text{m s}^{-1}$. If the Young's modulus of the wire is $16\times10^{11}\ \text{N m}^{-2}$, the extension of the wire over its natural length is:
Answer: (A) $0.03$ mm
Mass per unit length: $\mu = \dfrac{6\times10^{-3}}{0.6} = 0.01$ kg/m.
Tension from $v = \sqrt{T/\mu}$: $T = \mu v^2 = 0.01\times8100 = 81$ N.
$$\Delta l = \frac{Tl}{AY} = \frac{81\times0.6}{10^{-6}\times16\times10^{11}} = \frac{48.6}{1.6\times10^6} \approx 3.0\times10^{-5}\ \text{m} = 0.03\ \text{mm}$$
(The official answer key lists $0.02$ mm.)
Solution by Sreeraj P, M.Sc Physics