The speed of a transverse wave passing through a string of length 50 cm and mass 10g 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_______. A

Vw=Tμ60=T10×10−3×0.5T=(60)2×10−20.5=72NΔl=FlAY=72×0.52×10−6×1.2×1011=72×524×10−5=15×10−5

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The speed of a transverse wave passing through a string of length 50 cm and mass 10g 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_______. A

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answer is 15.

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Detailed Solution

$\begin{array}{l} V_{w} = \sqrt{\frac{T}{μ}} \\ 60 = \sqrt{\frac{T}{10 \times 10^{- 3}} \times 0 .5} \\ T = \frac{(60)^{2} \times 10^{- 2}}{0 .5} = 72 N \\ Δl = \frac{Fl}{AY} = \frac{72 \times 0 .5}{2 \times 10^{- 6} \times 1 .2 \times 10^{11}} \\ = \frac{72 \times 5}{24} \times 10^{- 5} = 15 \times 10^{- 5} \end{array}$