A spherical ball contracts in volume by `0.001%` when it is' subjected to a pressure of `100` atmosphere Calculate its bulk modulus.

Explanation

To calculate the bulk modulus of the spherical ball that contracts in volume by 0.001% under a pressure of 100 atmospheres, we can follow these steps:

### Step 1: Understand the given values
- The volume contraction is given as \(0.001\%\).
- The pressure applied is \(100\) atmospheres.

### Step 2: Convert the volume contraction percentage to a decimal
To express \(0.001\%\) as a decimal:
\[ 0.001\% = \frac{0.001}{100} = 0.00001 \]

### Step 3: Calculate the change in volume (ΔV)
If we denote the original volume as \(V\), then the change in volume (\(ΔV\)) can be expressed as:
\[ ΔV = 0.00001 \times V \]

### Step 4: Calculate the strain
Strain is defined as the change in volume divided by the original volume:
\[ \text{Strain} = \frac{ΔV}{V} = \frac{0.00001 \times V}{V} = 0.00001 \]

### Step 5: Use the formula for bulk modulus (K)
The bulk modulus (\(K\)) is defined as the ratio of pressure change to the strain:
\[ K = \frac{\text{Pressure}}{\text{Strain}} \]
Substituting the values we have:
\[ K = \frac{100 \text{ atmospheres}}{0.00001} \]

### Step 6: Calculate the bulk modulus
Now, perform the calculation:
\[ K = \frac{100}{0.00001} = 10000000 \text{ atmospheres} \]
This can also be expressed as:
\[ K = 10^7 \text{ atmospheres} \]

Thus, the bulk modulus of the spherical ball is \(10^7\) atmospheres.

### Summary of the Solution
The bulk modulus \(K\) of the spherical ball is \(10^7\) atmospheres.

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