The compressibility of water is $6 \times 10^{-10} \mathrm{~m}^{2} / \mathrm{N}$. If one litre of water is…

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
  1. 10
  2. 20
  3. 24
  4. 15

Solution

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 $=24 \times 10^{-3} \times 10^{3} \mathrm{~cm}^{3}$ $=24 \mathrm{~cc}$ .

Asked in: MHT CET 2020 (20 Oct Shift 1)

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