The speed of a transverse wave passing through a string of length 60 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________.

m = 10g

$\mathcal{l}=50cm$

A = 2mm²

Y = 1.2 × 10¹¹N/m²

$\Delta x=x\times 10^{-5}m$

As,  $\frac{T}{A}=Y\frac{\Delta x}{\mathcal{l}}$

$\Delta x=\frac{T\mathcal{l}}{AY}$

$T\mathcal{l}=V^{2}m$

= $\frac{V^{2}m}{AY}$

$=\frac{3600\times 10\times 10^{-3}}{2\times 10^{-6}\times 1.2\times 10^{11}}=\frac{1800\times 10^{-3}\times 10^6}{1.2}$

$=\frac{18}{12}\times 10^{-4}=\frac{3}{2}\times 10^{-4}=15\times 10^{-5}m$

So, x = 15

<p>m = 10g</p><p><math><mrow><mi mathvariant="script">l</mi><mo>=</mo><mn>5</mn><mn>0</mn><mi>c</mi><mi>m</mi></mrow></math></p><p>A = 2mm²</p><p>Y = 1.2 × 10¹¹N/m²</p><p><math><mrow><mi>Δ</mi><mi>x</mi><mo>=</mo><mi>x</mi><mo>×</mo><mn>1</mn><msup><mrow><mn>0</mn></mrow><mrow><mo>−</mo><mn>5</mn></mrow></msup><mi>m</mi></mrow></math></p><p>As, &nbsp;<math><mrow><mfrac><mrow><mi>T</mi></mrow><mrow><mi>A</mi></mrow></mfrac><mo>=</mo><mi>Y</mi><mfrac><mrow><mi>Δ</mi><mi>x</mi></mrow><mrow><mi mathvariant="script">l</mi></mrow></mfrac></mrow></math></p><p><math><mrow><mi>Δ</mi><mi>x</mi><mo>=</mo><mfrac><mrow><mi>T</mi><mi mathvariant="script">l</mi></mrow><mrow><mi>A</mi><mi>Y</mi></mrow></mfrac></mrow></math></p><p><math><mrow><mi>T</mi><mi mathvariant="script">l</mi><mo>=</mo><msup><mrow><mi>V</mi></mrow><mrow><mn>2</mn></mrow></msup><mi>m</mi></mrow></math></p><p>=&nbsp;<math><mrow><mfrac><mrow><msup><mrow><mi>V</mi></mrow><mrow><mn>2</mn></mrow></msup><mi>m</mi></mrow><mrow><mi>A</mi><mi>Y</mi></mrow></mfrac></mrow></math></p><p><math><mrow><mo>=</mo><mfrac><mrow><mn>3</mn><mn>6</mn><mn>0</mn><mn>0</mn><mo>×</mo><mn>1</mn><mn>0</mn><mo>×</mo><mn>1</mn><msup><mrow><mn>0</mn></mrow><mrow><mo>−</mo><mn>3</mn></mrow></msup></mrow><mrow><mn>2</mn><mo>×</mo><mn>1</mn><msup><mrow><mn>0</mn></mrow><mrow><mo>−</mo><mn>6</mn></mrow></msup><mo>×</mo><mn>1</mn><mo>.</mo><mn>2</mn><mo>×</mo><mn>1</mn><msup><mrow><mn>0</mn></mrow><mrow><mn>1</mn><mn>1</mn></mrow></msup></mrow></mfrac><mo>=</mo><mfrac><mrow><mn>1</mn><mn>8</mn><mn>0</mn><mn>0</mn><mo>×</mo><mn>1</mn><msup><mrow><mn>0</mn></mrow><mrow><mo>−</mo><mn>3</mn></mrow></msup><mo>×</mo><mn>1</mn><msup><mrow><mn>0</mn></mrow><mrow><mn>6</mn></mrow></msup></mrow><mrow><mn>1</mn><mo>.</mo><mn>2</mn></mrow></mfrac></mrow></math></p><p><math><mrow><mo>=</mo><mfrac><mrow><mn>1</mn><mn>8</mn></mrow><mrow><mn>1</mn><mn>2</mn></mrow></mfrac><mo>×</mo><mn>1</mn><msup><mrow><mn>0</mn></mrow><mrow><mo>−</mo><mn>4</mn></mrow></msup><mo>=</mo><mfrac><mrow><mn>3</mn></mrow><mrow><mn>2</mn></mrow></mfrac><mo>×</mo><mn>1</mn><msup><mrow><mn>0</mn></mrow><mrow><mo>−</mo><mn>4</mn></mrow></msup><mo>=</mo><mn>1</mn><mn>5</mn><mo>×</mo><mn>1</mn><msup><mrow><mn>0</mn></mrow><mrow><mo>−</mo><mn>5</mn></mrow></msup><mi>m</mi></mrow></math></p><div class="photo-widget-full"><div class="figure"><picture><source srcset="" media=" (max-width: 500px)"><img src="https://images.shiksha.com/mediadata/images/1753363966phpiIGBXU.jpeg" alt="" width="251" height="84" loading="lazy"></picture></div></div><p>So, x = 15</p>

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