Question

If the average depth of an ocean is 4000 m and the bulk modulus of water is \( 2 \times 10^9 \, \text{N/m}^2 \), then the fractional compression \( \frac{\Delta V}{V} \) of water at the bottom of the ocean is \( \alpha \times 10^{-2} \). The value of \( \alpha \) is ______ (Given \( g = 10 \, \text{m/s}^2 \), \( p = 1000 \, \text{kg/m}^3 \)).

Answer 1

Correct Answer: 2

The fractional compression \(\frac{\Delta V}{V}\) is given by:

\[ \frac{\Delta V}{V} = -\frac{\Delta P}{B} \]

The pressure \(\Delta P\) at the bottom of the ocean is:

\[ \Delta P = \rho gh = 1000 \times 10 \times 4000 = 4 \times 10^7 \, \text{Pa} \]

Thus,

\[ \frac{\Delta V}{V} = -\frac{4 \times 10^7}{2 \times 10^9} = -2 \times 10^{-2} \]

Therefore, \(\alpha = 2\).