Question

An object is located $2km$ beneath the surface of the water. If the fractional compression$∆V/V$is $1.36\%$ , the ratio of hydraulic stress to the corresponding hydraulic strain will be ……..

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

Answer 1

The correct option is D

$1.44\times {10}^{9}N{m}^{-2}$

Step 1. Given data :

$Densityofwater=1000kg{m}^{-3}$

$g=9.8m{s}^{-2}$

$Fractionalcompression,$ $∆V/V=1.36\%$

$Height,$$h=2km$

Step 2. Find Bulk modulus :

$\beta =\Delta p/(\Delta V/V)$

The pressure exerted by a column of liquid of height $h$ and density $\rho$ is given by the hydrostatic pressure equation $p=pgh$, where $g$ is the gravitational acceleration.

$\beta =\frac{\rho gh}{(∆V/V)}=\frac{1000\times 9.8\times 2\times {10}^3}{136/100}$

$\beta =1.44\times {10}^{9}N/m^2$

Hence , (D) is the correct option.