If Y, K and $\eta$ are the values of Young's modulus, bulk modulus and modulus of rigidity of any material respectively. Choose the correct relation for these parameters.
Solution
We know that,<br/><br/>$Y = 3K(1 - 2\sigma )$<br/><br/>$\Rightarrow \sigma = {1 \over 2}\left( {1 - {Y \over {3K}}} \right)$ ..... (i)<br/><br/>Also, $Y = 2\eta (1 + \sigma )$<br/><br/>$\Rightarrow \sigma = {Y \over {2\eta }} - 1$ .... (ii)<br/><br/>On comparing Eqs. (i) and (ii), we get<br/><br/>$\left( {1 - {Y \over {3K}}} \right){1 \over 2} = {Y \over {2\eta }} - 1$<br/><br/>On solving, we get<br/><br/>$K = {{\eta Y} \over {9\eta - 3Y}}$ N/m<sup>2</sup>
About this question
Subject: Physics · Chapter: Properties of Solids and Liquids · Topic: Elasticity
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