Question

If the longitudinal strain in a cubical body is three times the lateral strain then the bulk modulus $K$, Young's modulus $Y$ and rigidity $\eta$ are related by :

• A. $K=Y$
• B. $\eta =\frac{3Y}{8}$
• C. $Y=\frac{3\eta }{8}$
• D. $Y=\eta$

Answer 1

Answer: (A), (B)

The correct options are
A $K=Y$
B $\eta =\frac{3Y}{8}$

Poisson's ratio $=\frac{\text{lateral strain}}{\text{longitudinal strain}}$
$\sigma =\frac{1}{3}$
The relation among, $Y,K,\eta$ and $\sigma$
$Y=3K(1-2\sigma )$
$Y=3K(1-2\times \frac{1}{3})$
$Y=K$ and $Y=2\eta (1+\sigma )$
$Y=2\eta (1+\frac{1}{3})$
$Y=2\eta \left(\frac{4}{3}\right)=\frac{8}{3}\eta$
or $\eta =\frac{3Y}{8}$.