A) \[2.5\times {{10}^{10}}\,N/{{m}^{2}}\]
B) \[2.5\times {{10}^{11}}\,N/{{m}^{2}}\]
C) \[2.5\times {{10}^{9}}\,N/{{m}^{2}}\]
D) \[2.5\times {{10}^{15}}\,N/{{m}^{2}}\]
Correct Answer: A
Solution :
The bulk modulus [B] of a fluid is given by \[B=\frac{\Delta P}{\Delta V/V}=\frac{\Delta PV}{\Delta V}\] Given, \[V=1L=1000\,cc=1000\times {{10}^{-6}}{{m}^{3}}\] \[={{10}^{-3}}\,{{m}^{3}}\] \[\Delta P={{10}^{7}}\,N/{{m}^{2}},\,\,\Delta V=0.4c{{m}^{2}}=0.4\] \[c{{m}^{3}}=0.4\times {{10}^{-6}}{{m}^{3}}\] \[\therefore \] \[B=\frac{1\times {{10}^{7}}\times {{10}^{-3}}}{0.4\times {{10}^{-6}}}=\frac{1}{0.4}\times {{10}^{10}}\] \[\Rightarrow \] \[B=2.5\times {{10}^{10}}\,N/{{m}^{2}}\]
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