The volume contraction of a solid copper cube of edge length 10 cm, when subjected to a hydraulic pressure of 7 × 10⁶ Pa, would be __________ mm³. (Given bulk modulus of copper = 1.4 × 10¹¹ N m⁻²) Numerical answer type. Work it out, then open the answer.

Answer: 50. Δ V = PV/B, with V = (0.1)³ = 10⁻³ m³. Δ V = 7×10⁶×10⁻³1.4×10¹¹ = 5×10⁻⁸ m³ 1 m³ = 10⁹ mm³ ⇒ Δ V = 50 mm³ So the answer is 50 mm³.

The volume contraction of a solid copper cube of edge length 10 cm… | JEE Main 2025 (28 Jan, Shift 2)

Q3JEE Main 2025 · 28 JAN · SHIFT 2Easy

Bulk Modulus & Compressibility

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

(Given bulk modulus of copper $= 1.4 \times 10^{11}\text{ N m}^{-2}$ )

Numerical answer type. Work it out, then open the answer.

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Answer: 50

$\Delta V = \frac{PV}{B}$ , with $V = (0.1)^3 = 10^{-3}\ \text{m}^3$ .
$\Delta V = \frac{7\times10^{6}\times10^{-3}}{1.4\times10^{11}} = 5\times10^{-8}\ \text{m}^3$
$1\ \text{m}^3 = 10^{9}\ \text{mm}^3 \Rightarrow \Delta V = 50\ \text{mm}^3$
So the answer is $50\ \text{mm}^3$ .

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