Solveeit Logo
Login

Question

Question: The volume change of a solid copper cube 10 cm on an edge, when subjected to a pressure of 7 MPa is ...

The volume change of a solid copper cube 10 cm on an edge, when subjected to a pressure of 7 MPa is (Bulk modulus of copper = 140 GPa)

A

5×10−2 cm35 \times 10^{- 2}\text{ c}\text{m}^{3}

B

10×10−2 cm310 \times 10^{- 2}\text{ c}\text{m}^{3}

C

15×10−2 cm315 \times 10^{- 2}\text{ c}\text{m}^{3}

D

20×10−2 cm320 \times 10^{- 2}\text{ c}\text{m}^{3}

Answer

5×10−2 cm35 \times 10^{- 2}\text{ c}\text{m}^{3}

Explanation

Solution

: Here, L=10cm=10×10−2mL = 10cm = 10 \times 10^{- 2}m

P=7MPa=7×106PaP = 7MPa = 7 \times 10^{6}Pa

B=140GPa=140×109PaB = 140GPa = 140 \times 10^{9}Pa

AsB=PΔV/VB = \frac{P}{\Delta V/V}

∴ΔV=pVB=PL3B=(7×106Pa)(10×10−2m)3140×109Pa\therefore\Delta V = \frac{pV}{B} = \frac{PL^{3}}{B} = \frac{(7 \times 10^{6}Pa)(10 \times 10^{- 2}m)^{3}}{140 \times 10^{9}Pa}

=5×10−8m3=5×102cm3= 5 \times 10^{- 8}m^{3} = 5 \times 10^{2}cm^{3}