The volume contraction of a solid copper cube | vedclass

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(B) The formula for bulk modulus $B$ is given by $B = \frac{\Delta P}{\Delta V / V}$,where $\Delta P$ is the change in pressure,$V$ is the initial vol

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$50$

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(B) The formula for bulk modulus $B$ is given by $B = \frac{\Delta P}{\Delta V / V}$,where $\Delta P$ is the change in pressure,$V$ is the initial volume,and $\Delta V$ is the change in volume.Given: Edge length $L = 10 \ cm = 0.1 \ m$. Initial volume $V = L^3 = (0.1 \ m)^3 = 10^{-3} \ m^3$.Pressure change $\Delta P = 7 	imes 10^6 \ Pa$.Bulk modulus $B = 1.4 	imes 10^{11} \ Nm^{-2}$.Rearranging the formula for volume contraction $\Delta V$: $\Delta V = \frac{\Delta P 	imes V}{B}$.Substituting the values: $\Delta V = \frac{7 	imes 10^6 	imes 10^{-3}}{1.4 	imes 10^{11}} = \frac{7 	imes 10^3}{1.4 	imes 10^{11}} = 5 	imes 10^{-8} \ m^3$.Since $1 \ m^3 = 10^9 \ mm^3$,we convert the volume: $\Delta V = 5 	imes 10^{-8} 	imes 10^9 \ mm^3 = 50 \ mm^3$.

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 $= 1.4 \times 10^{11} \ Nm^{-2}$)

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