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JEE Main 2021 (17 Mar, Shift 2) · Density, Compressibility & Pascal's Law

Density, Compressibility & Pascal's Law question from JEE Main 2021 (17 Mar, Shift 2)

Q17JEE Main 2021 · 17 MAR · SHIFT 2Medium

Density, Compressibility & Pascal's Law

An object is located at 2 km beneath the surface of the water. If the fractional compression ΔVV\frac{\Delta V}{V} is 1.36%, the ratio of hydraulic stress to the corresponding hydraulic strain will be ____________. [Given: density of water is 1000 kgm−3{}^{-3} and g = 9.8 ms−2{}^{-2}]

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Answer: (b)

  1. Hydraulic stress =ρgh=1000×9.8×2000=1.96×107= \rho g h = 1000 \times 9.8 \times 2000 = 1.96 \times 10^{7} Pa.
  2. Stress/strain is the bulk modulus: B=ρghΔV/V=1.96×1070.0136B = \dfrac{\rho g h}{\Delta V/V} = \dfrac{1.96 \times 10^{7}}{0.0136}
  3. B≈1.44×109 N m−2B \approx 1.44 \times 10^{9}\ \text{N m}^{-2}
  4. So the answer is (b) 1.44×109 N m−21.44 \times 10^{9}\ \text{N m}^{-2}.
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