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(C) Given,edge of solid copper cube,$l = 7 \,cm$. Volume of the cube,$V = l^3 = (7 \,cm)^3 = 343 \,cm^3 = 343 	imes 10^{-6} \,m^3$. Hydraulic pressur

Vedclass · Accepted Answer

$19.6 	imes 10^{-3} \,cm^3$

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(C) Given,edge of solid copper cube,$l = 7 \,cm$. Volume of the cube,$V = l^3 = (7 \,cm)^3 = 343 \,cm^3 = 343 	imes 10^{-6} \,m^3$. Hydraulic pressure,$p = 8000 \,kPa = 8000 	imes 10^3 \,Pa = 8 	imes 10^6 \,Pa$. Bulk modulus of copper,$\beta = 140 \,GPa = 140 	imes 10^9 \,Pa$. We know that the Bulk modulus is given by $\beta = \frac{p}{\Delta V / V}$,where $\Delta V$ is the change in volume. Rearranging for $\Delta V$,we get $\Delta V = \frac{p V}{\beta}$. Substituting the values: $\Delta V = \frac{(8 	imes 10^6 \,Pa) 	imes (343 	imes 10^{-6} \,m^3)}{140 	imes 10^9 \,Pa} = \frac{2744}{140 	imes 10^9} \,m^3 = 19.6 	imes 10^{-9} \,m^3$. Converting back to $cm^3$: $1 \,m^3 = 10^6 \,cm^3$,so $\Delta V = 19.6 	imes 10^{-9} 	imes 10^6 \,cm^3 = 19.6 	imes 10^{-3} \,cm^3$.

$A$ solid copper cube of $7 \,cm$ edge is subjected to a hydraulic pressure of $8000 \,kPa$. The volume contraction of the copper cube is (Bulk modulus of copper $= 140 \,GPa$)

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