MHT CET · Physics · Mechanical Properties of Solids
The compressibility of water is \(6 \times 10^{-10} \mathrm{~m}^{2} / \mathrm{N}\). If one litre of water is subjected to a pressure of \(4 \times 10^{7} \mathrm{~N} / \mathrm{m}^{2}\), then the decrease in its volume in millilitre will be
- A 10
- B 20
- C 24
- D 15
Answer & Solution
Correct Answer
(C) 24
Step-by-step Solution
Detailed explanation
Bulk modulus \(B=-\frac{P}{\Delta V / V}\)
\(-\) ve sign shows that with an increase in pressure, a decrease in volume occurs
Compressibility \(\mathrm{K}=\frac{1}{\mathrm{~B}}=-\frac{\Delta \mathrm{V}}{\mathrm{PV}}\)
Decrease in volume,
\(\Delta \mathrm{V}=\mathrm{PVK}=4 \times 10^{7} \times 1 \times 6 \times 10^{-10}\)
\(=24 \times 10^{-3}\) litre \(=24 \times 10^{-3} \times 10^{3} \mathrm{~cm}^{3}\)
\(=24 \mathrm{~cc}\)
\(-\) ve sign shows that with an increase in pressure, a decrease in volume occurs
Compressibility \(\mathrm{K}=\frac{1}{\mathrm{~B}}=-\frac{\Delta \mathrm{V}}{\mathrm{PV}}\)
Decrease in volume,
\(\Delta \mathrm{V}=\mathrm{PVK}=4 \times 10^{7} \times 1 \times 6 \times 10^{-10}\)
\(=24 \times 10^{-3}\) litre \(=24 \times 10^{-3} \times 10^{3} \mathrm{~cm}^{3}\)
\(=24 \mathrm{~cc}\)
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