The volume contraction of a solid copper cube of edge length 10 cm, when subjected to a hydraulic pressure of , would be _______ . [2025]

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Solution

Q.
The volume contraction of a solid copper cube of edge length 10 cm, when subjected to a hydraulic pressure of $7 \times 10^{6} Pa$ , would be _______ ${mm}^{3}$ .

(Given bulk modulus of copper = $1.4 \times 10^{11}$ ${Nm}^{- 2}$ ) [2025]

Ans.
(50)

$B = - \frac{△ P}{\frac{△ V}{V}} = - \frac{V △ P}{△ V}$

$\Rightarrow △ V = - V \frac{△ P}{B} = {- (100 mm)}^{3} \times \frac{7 \times 10^{6} Pa}{1.4 \times 10^{11} N / m^{2}} = - 50 {mm}^{3}$

$\Rightarrow | △ V | = 50 {mm}^{3}$

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