Question:
An object is located at 2 km beneath the surface of the water. If the fractional compression \(\frac{\Delta V}{V}\) is 1.36%, the ratio of hydraulic stress to the corresponding hydraulic strain will be ____________. [Given : density of water is 1000 kgm-3 and g = 9.8 ms-2]
An object is located at 2 km beneath the surface of the water. If the fractional compression \(\frac{\Delta V}{V}\) is 1.36%, the ratio of hydraulic stress to the corresponding hydraulic strain will be ____________. [Given : density of water is 1000 kgm-3 and g = 9.8 ms-2]
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The hydraulic stress is the extra pressure \(\rho g h\); the stress-to-strain ratio is the bulk modulus.
Updated On: Nov 4, 2026
- \(1.44\times10^{7}\ \mathrm{Nm^{-2}}\)
- \(1.44\times10^{9}\ \mathrm{Nm^{-2}}\)
- \(1.96\times10^{7}\ \mathrm{Nm^{-2}}\)
- \(2.26\times10^{9}\ \mathrm{Nm^{-2}}\)
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The Correct Option is B
Solution and Explanation
Hydraulic stress: \(\Delta P = \rho g h = 1000\times9.8\times2000 = 1.96\times10^{7}\ \mathrm{N\,m^{-2}}\).
Hydraulic strain: \(\frac{\Delta V}{V} = 1.36\% = 1.36\times10^{-2}\).
Ratio = bulk modulus \(B = \frac{1.96\times10^{7}}{1.36\times10^{-2}} = 1.44\times10^{9}\ \mathrm{N\,m^{-2}}\).
Answer: (2) \(1.44\times10^{9}\ \mathrm{Nm^{-2}}\)
Hydraulic strain: \(\frac{\Delta V}{V} = 1.36\% = 1.36\times10^{-2}\).
Ratio = bulk modulus \(B = \frac{1.96\times10^{7}}{1.36\times10^{-2}} = 1.44\times10^{9}\ \mathrm{N\,m^{-2}}\).
Answer: (2) \(1.44\times10^{9}\ \mathrm{Nm^{-2}}\)
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