Question

An object is located at $2\text{km}$ 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 $1000{\text{kg m}}^{-3}$ and $g=9.8{\text{m s}}^{-2}$]

• A. $2.26\times {10}^9{\text{Nm}}^{-2}$
• B. $1.96\times {10}^7{\text{Nm}}^{-2}$
• C. $1.44\times {10}^7{\text{Nm}}^{-2}$
• D. $1.44\times {10}^9{\text{Nm}}^{-2}$

Answer 1

The correct option is D $1.44\times {10}^9{\text{Nm}}^{-2}$

Bulk modulus,
$$B=\frac{\Delta p}{\frac{\Delta V}{V}}$$$B=\frac{\rho gh}{\frac{\Delta V}{V}}=\frac{1000\times 9.8\times 2\times {10}^3}{\frac{1.36}{100}}$

$B=1.44\times {10}^9{\text{Nm}}^{-2}$