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MHT CET · Physics · Mechanical Properties of Fluids

The compressibility of water is \(5 \times 10^{-10} \mathrm{~m}^{2} / \mathrm{N}\). Pressure of \(15 \times 10^{6} \mathrm{~Pa}\) is applied
on \(100 \mathrm{ml}\) volume of water. The change in the volume of water is

  1. A \(0.75 \mathrm{ml}\) increase.
  2. B \(1.50 \mathrm{ml}\) increase.
  3. C \(0.75 \mathrm{ml}\) decrease.
  4. D zero.
Verified Solution

Answer & Solution

Correct Answer

(C) \(0.75 \mathrm{ml}\) decrease.

Step-by-step Solution

Detailed explanation

(A)
Given,
\(\begin{array}{l}
\beta=\frac{1}{\mathrm{~K}}=5 \times 10^{-10} \mathrm{~m}^{2} / \mathrm{N} \\
\Delta \mathrm{P}=15 \mathrm{MPa}=15 \times 10^{6} \mathrm{~Pa}
\end{array}\)
Bulk modulus,
\(\mathrm{K}=-\frac{\Delta \mathrm{P}}{\varepsilon_{\mathrm{V}}}\)
where, \(\varepsilon_{\mathrm{V}}=\) volumetric strain
\(\begin{array}{l}
\beta=-\frac{\varepsilon_{\mathrm{V}}}{\Delta \mathrm{P}} \\
\varepsilon_{\mathrm{V}}=-\beta \Delta \mathrm{P}=-5 \times 10^{-10} \times 15 \times 10^{6} \\
\varepsilon_{\mathrm{V}}=7.5 \times 10^{-3}
\end{array}\)
The correct option is A.