Question

A $200\times 100\times 50mm$ steel block is subjected to a hydorstatic pressure of $15MPa.$ The Young's modulus and Poisson's ratio of the material are $200GPa$ and 0.3 respectively. The change in the volume of the block in $m{m}^3$ is

• A. $85$
• B. $90$
• C. $100$
• D. $110$

Answer 1

The correct option is B $90$

$V=a\times b\times c$
$=200\times 100\times 50m{m}^3$
$={10}^{6}m{m}^3$
$E=200GPa,$ $\mu =0.3$
$\frac{dV}{V}=\frac{3\sigma }{E}(1-2\mu )$
$dV=\frac{3\sigma }{E}(1-2\mu )\times V$
$=\frac{3\times 15}{200\times {10}^3}\times \{1-(2\times 0.3\left)\right\}\times {10}^6$
$=90m{m}^3$