The volume contraction of a solid copper cube of edge length 10 cm , when subjected to a hydraulic pressure…

The volume contraction of a solid copper cube of edge length 10 cm , when subjected to a hydraulic pressure of $7 \times 10^6 \mathrm{~Pa}$, would be ____ $\mathrm{mm}^3$.
(Given bulk modulus of copper $=1.4 \times 10^{11} \mathrm{~N} \mathrm{~m}^{-2}$)

Solution

$\begin{aligned} & \mathrm{B}=\frac{\Delta \mathrm{P}}{\frac{\Delta \mathrm{V}}{\mathrm{V}}} \\ & \Delta \mathrm{V}=\frac{7 \times 10^6}{1.4 \times 10^{11}} \times\left(10 \times 10^{-2}\right)^3 \\ & \Delta \mathrm{~V}=50 \mathrm{~mm}^3\end{aligned}$

Asked in: JEE Main 2025 (28 Jan Shift 2)

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