Question

The increase in pressure required to decrease the volume of $200L$ of water by $0.004\%$ is (Bulk modulus of water is $2.1\times {10}^{9}N/m^2$)

• A. $8.4\times {10}^{4}N/m^2$
• B. $8.4\times {10}^{3}N/m^2$
• C. $8.4\times {10}^{5}N/m^2$
• D. $8.4\times {10}^{6}N/m^2$

Answer 1

The correct option is A $8.4\times {10}^{4}N/m^2$

decrease in volume $=0.004\%$

$\frac{\Delta V}{V}=4\times {10}^{-5}$

Bulk moduls of water $=2.1\times {10}^9{Nm}^{-1}$

$\begin{array}{cc}\Rightarrow \left|\frac{P}{deltaV/V}\right|& =2.1\times {10}^9{Nm}^{-1}\\ \Rightarrow P& =2.1\times {10}^9\times \frac{\Delta V}{V}\\ & =2.1\times {10}^9\times 4\times {10}^{-5}\\ P& =8.4\times {10}^4{Nm}^{-2}\end{array}$