The relation between , , and K for a elastic material is - Vidyadip

MCQ

The relation between $\gamma ,\,\eta $ and $K$ for a elastic material is

A
$\frac{1}{\eta } = \frac{1}{{3\gamma }} + \frac{1}{{9K}}$
B
$\frac{1}{K} = \frac{1}{{3\gamma }} + \frac{1}{{9\eta }}$
C
$\frac{1}{\gamma } = \frac{1}{{3K}} + \frac{1}{{9\eta }}$
✓
$\frac{1}{\gamma } = \frac{1}{{3\eta }} + \frac{1}{{9K}}$

✓

Answer

Correct option: D.

$\frac{1}{\gamma } = \frac{1}{{3\eta }} + \frac{1}{{9K}}$

d
$\mu=$ Modulus of Rigiditg

$k =$ Bulk Modulus.

$\sigma=$ Normal stress

$y =3 k (1-2 \sigma)-(1)$

$y =2 \eta(1+\alpha)-(2)$

$\frac{ y }{3 k }=1-2 \sigma-(3), \frac{ x }{2 \mu}=1+\sigma-(4)$

Multiply eq $4$ by $2$.

$\frac{ y }{3 k }+\frac{ y }{\mu}=3-(5)$

Adding equ" $(3)$ and eqn $(5)$

$\frac{ y }{3 k }+\frac{ y }{\mu}=3$

$\frac{1}{3 k }+\frac{1}{\mu}=\frac{3}{ y }$

$\frac{1}{ y }=\frac{1}{9 k }+\frac{1}{3 \mu}$

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