Class 11th Physics Mechanical Properties of Solids Maths NCERT Exemplar Solutions Class 11th Chapter Eleven Physics

If y, K and $η$ are the value of Young's modulus, bulk modulus of rigidity of any material respectively. Choose

Option 1 - <p><span class="mathml" contenteditable="false"> <math> <mrow> <mi>Y</mi> <mo>=</mo> <mfrac> <mrow> <mn>9</mn> <mi>K</mi> <mi>η</mi> </mrow> <mrow> <mn>2</mn> <mi>η</mi> <mo>+</mo> <mn>3</mn> <mi>K</mi> </mrow> </mfrac> <mi>N</mi> <mo>/</mo> <msup> <mrow> <mi>m</mi> </mrow> <mrow> <mn>2</mn> </mrow> </msup> </mrow> </math> </span></p>

Option 2 - <p><span class="mathml" contenteditable="false"> <math> <mrow> <mi>K</mi> <mo>=</mo> <mfrac> <mrow> <mi>Y</mi> <mi>η</mi> </mrow> <mrow> <mn>9</mn> <mi>η</mi> <mo>−</mo> <mn>3</mn> <mi>Y</mi> </mrow> </mfrac> <mi>N</mi> <mo>/</mo> <msup> <mrow> <mi>m</mi> </mrow> <mrow> <mn>2</mn> </mrow> </msup> </mrow> </math> </span></p>

Option 3 - <p><span class="mathml" contenteditable="false"> <math> <mrow> <mi>η</mi> <mo>=</mo> <mfrac> <mrow> <mn>3</mn> <mi>Y</mi> <mi>K</mi> </mrow> <mrow> <mn>9</mn> <mi>K</mi> <mo>+</mo> <mi>Y</mi> </mrow> </mfrac> <mi>N</mi> <mo>/</mo> <msup> <mrow> <mi>m</mi> </mrow> <mrow> <mn>2</mn> </mrow> </msup> </mrow> </math> </span></p>

Option 4 - <p><span class="mathml" contenteditable="false"> <math> <mrow> <mi>Y</mi> <mo>=</mo> <mfrac> <mrow> <mn>9</mn> <mi>K</mi> <mi>η</mi> </mrow> <mrow> <mn>3</mn> <mi>K</mi> <mo>−</mo> <mi>η</mi> </mrow> </mfrac> <mi>N</mi> <mo>/</mo> <msup> <mrow> <mi>m</mi> </mrow> <mrow> <mn>2</mn> </mrow> </msup> </mrow> </math> </span></p>

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Alok Kumar Singh | Contributor-Level 10

5 months ago

Correct Option - 2

Detailed Solution:

If $μ$ is Poisson's ratio,

Y = 3K (1 - 2 $μ$ ) ……… (1)

and Y = 2 $n (1 + μ)$ ……… (2)

With the help of equations (1) and (2), we can write

$\frac{3}{Y} = \frac{1}{η} + \frac{1}{3 k} \Rightarrow K = \frac{η Y}{9 η - 3 Y}$

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