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Determine the volume contraction of a solid copper cube, 10 \mathrm{~cm} on an edge, when subjected to a hydraulic pressure of 7.0 \times 10^{6} \mathrm{~Pa}.
CBSE | Class 11 | Mechanical Properties of Solids | NCERT | Physics
Determine the volume contraction of a solid copper cube, 10 \mathrm{~cm} on an edge, when subjected to a hydraulic pressure of 7.0 \times 10^{6} \mathrm{~Pa}.

Side of the copper cube is given as a=10 \mathrm{~cm}

Therefore, Volume of the copper cube will be,
\mathrm{V}=\mathrm{a}^{3}=10^{-3} \mathrm{~m}^{3}

Hydraulic pressure is given as \mathrm{p}=7.0 \times 10^{6} \mathrm{~Pa}

Bulk modulus of copper is given as \mathrm{B}=140 \mathrm{G} \mathrm{Pa}=140 \times 10^{9} \mathrm{~Pa}.

Bulk modulus, \mathrm{K}=-\mathrm{P} /(\Delta \mathrm{V} / \mathrm{V})

The value of volume contraction is, \Delta \mathrm{V}=-\mathrm{PV} / \mathrm{K} =-\left(7 \times 10^{6} \times 0.001\right) /\left(140 \times 10^{9}\right) =-0.05 \times 10^{-6} \mathrm{~m}^{3}

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