First slide

Elastic Modulie

Question

The approximate depth of an ocean is 2700 m. The compressibility of water is $45.4 \times 10^{- 11} {Pa}^{- 1} and density of water is 10^{3} kg / m^{3}$ . What fractional compression of water will be obtained at the bottom of the ocean?

Moderate

A

$0.8 \times 10^{- 2}$
B

1.0 $\times 10^{- 2}$
C

$1.2 \times 10^{- 2}$
D

$1.4 \times 10^{- 2}$

Solution

Bulk modulus |B| = $\frac{∆ p}{(\frac{∆ V}{V})}$
B = $\frac{1}{Compressibility (K)}$
$\frac{1}{K} = \frac{hρg}{(\frac{∆ V}{V})}$
$(\frac{∆ V}{V}) = (hρg) K$
$\Rightarrow \frac{∆ V}{V} = 2.7 \times 10^{3} \times 10^{3} \times 10 \times 45.4 \times 10^{- 11}$
= $1.23 \times 10^{- 2}$

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