The presssure of a medium is changed from `1.01xx10^(5) Pa` to ` 1.165xx10^(5) Pa` and change in volume is `10 % ` keeping temperature constant . The bulk modulus of the medium is
(a) `204.8 xx 10^(5) Pa` (b) `102.4xx10^(5) Pa` (c ) `5.12xx10^(5) Pa`
(d) `1.55xx10^(5) Pa`

Explanation

To find the bulk modulus of the medium given the change in pressure and volume, we can follow these steps:

### Step 1: Identify the initial and final pressures
- Initial pressure, \( P_1 = 1.01 \times 10^5 \, \text{Pa} \)
- Final pressure, \( P_2 = 1.165 \times 10^5 \, \text{Pa} \)

### Step 2: Calculate the change in pressure
The change in pressure (\( \Delta P \)) can be calculated using the formula:
\[ \Delta P = P_2 - P_1 \]
Substituting the values:
\[ \Delta P = 1.165 \times 10^5 \, \text{Pa} - 1.01 \times 10^5 \, \text{Pa} = 0.155 \times 10^5 \, \text{Pa} \]

### Step 3: Determine the volumetric strain
The change in volume is given as 10%, which means:
\[ \text{Volumetric strain} = \frac{\Delta V}{V} = -0.1 \]
(Note: The negative sign indicates a decrease in volume.)

### Step 4: Use the formula for bulk modulus
The bulk modulus (\( K \)) is defined as:
\[ K = -\frac{\Delta P}{\text{Volumetric strain}} \]
Substituting the values we have:
\[ K = -\frac{0.155 \times 10^5 \, \text{Pa}}{-0.1} \]

### Step 5: Calculate the bulk modulus
\[ K = \frac{0.155 \times 10^5}{0.1} = 1.55 \times 10^5 \, \text{Pa} \]

### Step 6: Match the result with the options provided
The calculated bulk modulus is \( 1.55 \times 10^5 \, \text{Pa} \), which corresponds to option (d).

### Final Answer:
The bulk modulus of the medium is \( 1.55 \times 10^5 \, \text{Pa} \).

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