Choose the correct relationship between Poisson ratio ( ). bulk m… - Vidyadip

MCQ

Choose the correct relationship between Poisson ratio $(\sigma)$. bulk modulus $( K )$ and modulus of rigidity $(\eta)$ of a given solid object:

✓
$\sigma=\frac{3 K -2 \eta}{6 K +2 \eta}$
B
$\sigma=\frac{6 K +2 \eta}{3 K -2 \eta}$
C
$\sigma=\frac{3 K+2 \eta}{6 K+2 \eta}$
D
$\sigma=\frac{6 K -2 \eta}{3 K -2 \eta}$

✓

Answer

Correct option: A.

$\sigma=\frac{3 K -2 \eta}{6 K +2 \eta}$

a
$Y =3 \eta(1+\sigma)$

$Y =3 K (1-\sigma)$

$\Rightarrow 2 \eta(1+\sigma)=3 K (1-2 \sigma)$

$\Rightarrow \sigma=\left(\frac{3 K -2 \eta}{6 K +2 \eta}\right)$

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