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.
Correct Option: 1
(1)
$\Rightarrow y=3 k(1-2 \sigma)$
$\Rightarrow \sigma=\frac{1}{2}\left(1-\frac{y}{3 k}\right)$
$\Rightarrow y=2 \eta(1+\sigma)$
$\Rightarrow \sigma=\frac{y}{2 \eta}-1 \quad \ldots(2)$
by comparing equation (1) and (2), we get
$\Rightarrow \frac{y}{2 \eta}-1=\frac{1}{2}\left(1-\frac{y}{3 k}\right)$
$\Rightarrow \frac{y}{\eta}-2=1-\frac{y}{3 k}$
$\Rightarrow \frac{y}{\eta}=1+2-\frac{y}{3 k} \Rightarrow \frac{y}{\eta}=3-\frac{y}{3 k}$
$\Rightarrow \frac{y}{3 k}=3-\frac{y}{\eta} \Rightarrow \frac{y}{3 k}=\frac{3 \eta-y}{\eta}$
$\Rightarrow k=\frac{\eta y}{9 \eta-3 y}$
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