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Physics Question on elastic moduli

A solid copper cube of 7 cm7 \,cm edge is subjected to a hydraulic pressure of 8000 kPa8000\, kPa. The volume contraction of the copper cube is (Bulk modulus of copper = 140 GPa140 \,GPa )

A

196×10−3cm3 196 \times 10^{-3} cm^3

B

19.6×10−6cm3 19.6 \times 10^{-6} cm^3

C

19.6×10−3cm3 19.6 \times 10^{-3} cm^3

D

196×103cm3 196 \times 10^{3} cm^3

Answer

19.6×10−3cm3 19.6 \times 10^{-3} cm^3

Explanation

Solution

Given,
edge of solid copper cube, l=7 cml=7 \,cm
hydraulic pressure, p=8000 kPa=8000×103 Pap=8000 \,kPa =8000 \times 10^{3}\, Pa
and Bulk modulus of copper, β=140 GPa\beta=140\, GPa
=140×109 Pa=140 \times 10^{9} \,Pa
As we know that,
Bulk modulus, β=p(ΔVV)\beta=\frac{p}{\left(\frac{\Delta V}{V}\right)}
or β=pVΔV\beta=\frac{p V}{\Delta V}
∴ΔV=pVβ=8000×103×(l)3140×109\therefore \Delta V=\frac{p V}{\beta} =\frac{8000 \times 10^{3} \times(l)^{3}}{140 \times 10^{9}}
=8000×103×(7)3140×109=\frac{8000 \times 10^{3} \times(7)^{3}}{140 \times 10^{9}}
=19.6×10−3 cm3=19.6 \times 10^{-3} \,cm ^{3}