Question

A copper solid cube of 60 mm side is subjected to a pressure of $ 2.5\times {{10}^{7}}Pa. $ If the bulk modulus of copper is $ 1.25\times {{10}^{7}}N/{{m}^{2}}, $ the change in the volume of cube is:

• A. $ -\text{ }43.2\text{ }{{m}^{3}} $
• B. $ -\text{ }43.2\text{ }m{{m}^{3}} $
• C. $ -\text{ }43.2\text{ }c{{m}^{3}} $
• D. $ -\text{ }432\text{ }m{{m}^{3}} $

Answer 1

Answer: (B)

Bulk modulus $ K=\frac{PV}{\Delta V} $ $ \left( \begin{align} & \text{Given:} \\ & \text{Side}\,\text{of cube = 60}\,\text{cm} \\ & \text{P = 2}\text{.5}\times \text{1}{{\text{0}}^{7}}Pa \\ & K=1.25\times {{10}^{11}} \\ \end{align} \right) $ $ \Delta V=\frac{PV}{K} $ $ \Rightarrow $ $ \Delta V=\frac{2.5\times {{10}^{7}}\times 60\times 60\times 60}{1.25\times {{10}^{11}}} $ $ =-43.2\,m{{m}^{3}} $