Question

A rock element during deformation, experienced a pressure change of $5×10^4 N/m^2$, due to which its volume changed from 4 cm3 to 3.9 cm3. The bulk modulus of the rock is ________ ×$10^6 N/m^2$. (In integer)

Answer 1

Correct Answer: 2

Calculating the Bulk Modulus

Step 1: Understanding the Formula

The bulk modulus \( K \) is defined by the formula:

\[ K = \frac{\Delta P}{\frac{\Delta V}{V}} \]

Where:

• \(\Delta P\) is the pressure change.
• \(\Delta V\) is the change in volume.
• V is the initial volume.

Step 2: Given Values

Given:

• \(\Delta P = 5 \times 10^4 \, \text{N/m}^2\) 
• Initial volume \( V = 4 \, \text{cm}^3\)
• Final volume \( V' = 3.9 \, \text{cm}^3\)

Step 3: Calculate the Change in Volume

The change in volume \( \Delta V \) is calculated as:

\[ \Delta V = V' - V = 3.9 \, \text{cm}^3 - 4.0 \, \text{cm}^3 = -0.1 \, \text{cm}^3 \]

Step 4: Calculate the Volumetric Strain

The volumetric strain \( \frac{\Delta V}{V} \) is calculated as:

\[ \frac{\Delta V}{V} = \frac{-0.1 \, \text{cm}^3}{4.0 \, \text{cm}^3} = -0.025 \]

Step 5: Calculate the Bulk Modulus

Now, we can calculate the bulk modulus \( K \) by substituting the values into the formula:

\[ K = \frac{5 \times 10^4 \, \text{N/m}^2}{-0.025} = 2 \times 10^6 \, \text{N/m}^2 \]

Final Answer:

The bulk modulus of the rock is: 2 × 10⁶ N/m².