Question

A solid cube is subjected to a pressure of $(5\times {10}^{5}N/m^2)$. Each side of the cube is shortened by then volumetric strain and Bulk modulus of the cube are

• A. $0.03,5\times {10}^{5}N/m^2$
• B. $0.03,1.67\times {10}^{7}N/m^2$
• C. $3,1.67\times {10}^{-7}N/m^2$
• D. $0.01,1.67\times {10}^{7}N/m^2$

Answer 1

The correct option is A $0.03,5\times {10}^{5}N/m^2$

$P=5\times {10}^{5}N/m^2$, let initial side=$a$

$V=a^3$

Shortened side=$0.99a$

Shortened volume=$(0.99{)}^3{a}^3$

$B=\frac{-V△P}{△v}\Rightarrow \frac{-V\times 5{\times 10}^5}{-a^3(1-{\left(0.99\right)}^3)}\Rightarrow \frac{5{\times 10}^5}{0.030}\Rightarrow 166.66{\times 10}^5\Rightarrow 1.67{\times 10}^{7}N/m^3$

$\frac{△v}{V}=0.03\to$ Volumetric strain.