Question

A bar made of material whose Young's modulus is equal to $E$ and Poisson's ratio to $\mu$ is subjected to the hydrostatic pressure $p$. Find the relationship between the compressibility $\beta$ and the elastic constants $E$ and $\mu$.

• A. $\beta =(1-2\mu )\frac{3}{E}$
• B. $\beta =(1-3\mu )\frac{2}{E}$
• C. $\beta =(1+2\mu )\frac{E}{3}$
• D. $\mu =(1-2\beta )\frac{3}{E}$

Answer 1

The correct option is A $\beta =(1-2\mu )\frac{3}{E}$

We know,

$\frac{E}{3K}=1-2\mu$

$K$ = Bulk modulus.

Also, Compressibility $\beta =\frac{1}{K}$

$\therefore \frac{E\beta }{3}-1-2\mu$

$\therefore \beta =\frac{3}{E}(1-2\mu )$