A spherical ball contracts in volume by 0.01% when subjected to a normal uniform pressure of 100 atmospheres. Calculate the bulk modulus of the meterial.

Explanation

To calculate the bulk modulus of the material of the spherical ball that contracts in volume by 0.01% under a pressure of 100 atmospheres, we will follow these steps:

### Step 1: Understand the formula for Bulk Modulus
The bulk modulus (K) is defined as the ratio of pressure change (ΔP) to the relative change in volume (ΔV/V). The formula is given by:
\[ K = -\frac{P}{\frac{\Delta V}{V}} \]

### Step 2: Identify the values from the problem
- The pressure (P) applied is 100 atmospheres.
- The change in volume (ΔV) is -0.01% (which is -0.0001 in decimal form).
- The relative change in volume (ΔV/V) can be calculated as:
\[ \frac{\Delta V}{V} = \frac{-0.01}{100} = -0.0001 \]

### Step 3: Convert pressure from atmospheres to Pascals
1 atmosphere is equivalent to 101325 Pascals. Therefore, to convert 100 atmospheres to Pascals:
\[ P = 100 \times 101325 \, \text{Pa} = 10132500 \, \text{Pa} \]

### Step 4: Substitute values into the bulk modulus formula
Now substituting the values into the bulk modulus formula:
\[ K = -\frac{10132500}{-0.0001} \]

### Step 5: Calculate the bulk modulus
Calculating the above expression:
\[ K = \frac{10132500}{0.0001} = 1.01325 \times 10^{11} \, \text{Pa} \]

### Step 6: Final result
Thus, the bulk modulus of the material is:
\[ K \approx 1.013 \times 10^{11} \, \text{Pa} \]