The compressibility of water is 4 × 10^-5 per unit atmospheric pressure. The decrease in volume of 100 ~cm^3 of water under a pressure of 100 atmosphere will be

Correct answer: (A) 0.4 ~cm^3. Compressibility =1/(~B)=(Δ V / V)/P . Here, P=100 ~atm Compressibility =4 × 10^-5 and V=100 ~cm^3 Hence, Δ V=0.4 ~cm^3

Q123 / 125 · BITSAT 2021 · Physics

The compressibility of water is $4 \times 10^{-5}$ per unit atmospheric pressure. The decrease in volume of $100 \mathrm{~cm}^{3}$ of water under a pressure of 100 atmosphere will be

Correct answer
A
$0.4 \mathrm{~cm}^{3}$
B
$4 \times 10^{-5} \mathrm{~cm}^{3}$
C
$0.025 \mathrm{~cm}^{3}$
D
$0.004 \mathrm{~cm}^{3}$

Solution

Compressibility $=\frac{1}{\mathrm{~B}}=\frac{\Delta \mathrm{V} / \mathrm{V}}{\mathrm{P}}$. Here, $\mathrm{P}=100 \mathrm{~atm}$ Compressibility $=4 \times 10^{-5}$ and $\mathrm{V}=100 \mathrm{~cm}^{3}$ Hence, $\Delta \mathrm{V}=0.4 \mathrm{~cm}^{3}$

Hence, the correct answer is option: 'A'.

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