The average depth of an oil well is 2000 , m. | vedclass

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(A) The bulk modulus $B$ is defined as $B = -\frac{p}{\Delta V / V}$, where $p$ is the pressure and $\frac{\Delta V}{V}$ is the volumetric strain.Ther

Vedclass · Accepted Answer

$3.75$

Vedclass · Answer

(A) The bulk modulus $B$ is defined as $B = -\frac{p}{\Delta V / V}$, where $p$ is the pressure and $\frac{\Delta V}{V}$ is the volumetric strain.Therefore, the fractional compression is given by $-\frac{\Delta V}{V} = \frac{p}{B}$.The pressure at the bottom of the well is $p = ho g h$.Substituting the values: $ho = 1500 \, kg/m^3$, $g = 10 \, m/s^2$, $h = 2000 \, m$, and $B = 8 	imes 10^8 \, N/m^2$.Fractional compression (in $\%$) $= \frac{ho g h}{B} 	imes 100$.$= \frac{1500 	imes 10 	imes 2000}{8 	imes 10^8} 	imes 100$.$= \frac{3 	imes 10^7}{8 	imes 10^8} 	imes 100 = \frac{3}{80} 	imes 100 = 3.75 \%$.

The average depth of an oil well is $2000 \, m$. If the bulk modulus of oil is $8 \times 10^8 \, N/m^2$ and the density of oil is $1500 \, kg/m^3$, the fractional compression at the bottom of the well is (take $g = 10 \, m/s^2$): (in $\%$)

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