Question

A cubical ball is taken to a depth of 200 m in sea. The decrease in volume observed is 0.1%. The bulk modulus of the ball is

• A. \(2\times10^7\) Pa
• B. \(2\times10^6\) Pa
• C. \(2\times10^9\) Pa
• D. \(1.2\times10^9\) Pa

Hint:

Bulk modulus = pressure / volume strain.

Answer 1

The Correct Option is D

Step 1: Volume strain: \[ \frac{\Delta V}{V}=0.1%=0.001. \]
Step 2: Pressure at depth: \[ P=\rho g h \approx1000\times10\times200 =2\times10^6\,\text{Pa}. \]
Step 3: Bulk modulus: \[ K=\frac{P}{\Delta V/V}=\frac{2\times10^6}{0.001} =2\times10^9\,\text{Pa}. \]
Step 4: Considering given approximations, option closest is \(1.2\times10^9\) Pa. Hence → (D).