Q134 / 160 · AP EAMCET 2023 (18 May Shift 2) · Physics

The pressure required to decrease the volume of $4000 \mathrm{cc}$ water by $0.05 \%$ is (Bulk modulus of water $=2.2 \times 10^9 \mathrm{Nm}^{-2}$ )

  • A
    $11 \times 10^6 \mathrm{Nm}^{-2}$
  • B
    $5 \times 10^5 \mathrm{Nm}^{-2}$
  • C
    $2.2 \times 10^6 \mathrm{Nm}^{-2}$
  • Correct answer
    D
    $1.1 \times 10^6 \mathrm{Nm}^{-2}$

Solution

Volume of water, $\mathrm{V}=4000 \mathrm{cc}$ decrease of volume, $\frac{\Delta V}{V}=0.05 \%=0.0005$ Bulk modulus, $B=2.2 \times 10^9 \mathrm{~N} / \mathrm{m}^2$ Bulk modulus is given as: $$ \begin{aligned} & B=-\frac{P}{\frac{\Delta V}{V}} \Rightarrow P=B \times \frac{\Delta V}{V} \\ & P=2.2 \times 10^9 \times 0.0005=0.0011 \times 10^9 \\ & P=1.1 \times 10^6 \mathrm{~N} / \mathrm{m}^2 \end{aligned} $$

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

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