Question

The fractional compression \( \frac{\Delta V}{V} \) of water at the depth of 2.5 km below the sea level is:

• A. 1.5
• B. 1.0
• C. 1.75
• D. 1.25

Hint:

For problems involving pressure at depth, use the formula \( P = \rho g h \) and apply the bulk modulus to calculate fractional compression.

Answer 1

The Correct Option is A

The fractional compression \( \frac{\Delta V}{V} \) of a substance like water under pressure is given by \( \frac{\Delta V}{V} = \frac{P}{B} \), where \( P \) is the pressure at depth and \( B \) is the bulk modulus of water.
At a depth of 2.5 km, the pressure \( P = \rho g h \), where \( \rho \) is the density of water, \( g \) is the acceleration due to gravity, and \( h \) is the depth. Substituting the given values and calculating, we find the fractional compression is approximately 1.5.