Q134 / 160 · AP EAMCET 2024 (20 May Shift 2) · Physics

Depth of a river is 100 m . Magnitude of compressibility of the water is $0.5 \times 10^{-9} \mathrm{~N}^{-1} \mathrm{~m}^2$. The fractional compression in water at the bottom of the river is (Acceleration due to gravity $=10 \mathrm{~ms}^{-2}$ )

  • A
    $0.9 \times 10^3$
  • Correct answer
    B
    $0.5 \times 10^3$
  • C
    $2 \times 10^{-3}$
  • D
    $1.3 \times 10^{-2}$

Solution

Compressibility, $\mathrm{k}=0.5 \times 10^{-9} \mathrm{~N}^{-1} \mathrm{~m}^2$ Pressure, $\mathrm{P}=\delta \mathrm{gh}=10^3 \times 10 \times 100=10^6 \mathrm{Nm}^{-2}$ $\therefore \mathrm{K}=\frac{1}{\mathrm{~B}}=\frac{(\Delta \mathrm{v} / \mathrm{v})}{\mathrm{P}}$ $\therefore$ Fractional change in volume, $\frac{\Delta \mathrm{V}}{\mathrm{V}}=\mathrm{KP}=0.5 \times 10^{-9} \times 10^6=0.5 \times 10^{-3}$

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

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