If Y, K and η are the values of Young's modulus, bulk modulus and...

$Y -$Young's modulus, $K -$Bulk modulus, $η -$modulus of rigidity
We know that, $</p><p>$Y = 3k \left(1 - 2\sigma\right)$</p><p>$⇒ \sigma = \dfrac{1}{2}\left(1 - \dfrac{Y}{3k}\right)$. . . \left(1\right)$

$⇒ Y = 2η\left(1 + \sigma\right)⇒ \sigma = \dfrac{Y}{2η} -1 . . . \left(2\right)</p><p>From$ the $equation \left(1\right) and the equation \left(2\right)</p><p>\dfrac{1}{2}\left(1 - \dfrac{Y}{3k}\right)=\dfrac{Y}{2η}$ -$1$

$⇒ 1 - \dfrac{Y}{3k} = \dfrac{Y}{η} -$2⇒$\dfrac{Y}{3k}=3 - \dfrac{Y}{n}$⇒$\dfrac{Y}{3k}=\dfrac{3η - Y}{η}$

$⇒ \dfrac{ηY}{3k} =$3η - Y⇒ k =$\dfrac{ηY}{9η - 3Y}N${m}^{- 2}.