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QJEEM22Phed25: JEE Main 2022 Physics - Class 11 JEEM22Phed25 Solution: The speed of a transverse wave passing through a string of…

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 1.2×1011Nm−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 __________.

Step-by-Step Verified Solution

Vw=Tμ\mathrm{V}_{\mathrm{w}}=\sqrt{\frac{\mathrm{T}}{\mu}}

60=T10×10−3×0.560=\sqrt{\frac{\mathrm{T}}{10 \times 10^{-3}} \times 0.5}

 T=(60)2×10−20.5=72 N\mathrm{~T}=\frac{(60)^2 \times 10^{-2}}{0.5}=72 \mathrm{~N}

Δℓ=FℓAY=72×0.52×10−6×1.2×1011\Delta \ell=\frac{\mathrm{F} \ell}{\mathrm{AY}}=\frac{72 \times 0.5}{2 \times 10^{-6} \times 1.2 \times 10^{11}}

=72×524×10−5=15×10−5=\frac{72 \times 5}{24} \times 10^{-5}=15 \times 10^{-5}

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