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, we can follow these steps:

### Step 1: Identify the given data
- Initial pressure, \( P_1 = 1.01 \times 10^5 \, \text{Pa} \)
- Final pressure, \( P_2 = 1.165 \times 10^5 \, \text{Pa} \)
- Change in volume percentage, \( \frac{\Delta V}{V} \times 100 = -10\% \)

### Step 2: Calculate the change in pressure
The change in pressure, \( \Delta P \), is given by:
\[ \Delta P = P_2 - P_1 \]
Substituting the values:
\[ \Delta P = (1.165 \times 10^5) - (1.01 \times 10^5) = 0.155 \times 10^5 \, \text{Pa} = 1.55 \times 10^4 \, \text{Pa} \]

### Step 3: Calculate the volumetric strain
The volumetric strain, \( \frac{\Delta V}{V} \), can be calculated from the percentage change in volume:
\[ \frac{\Delta V}{V} = \frac{-10}{100} = -0.1 \]

### Step 4: Use the formula for bulk modulus
The bulk modulus \( B \) is defined as:
\[ B = -\frac{\Delta P}{\frac{\Delta V}{V}} \]
Substituting the values we calculated:
\[ B = -\frac{1.55 \times 10^4}{-0.1} = \frac{1.55 \times 10^4}{0.1} = 1.55 \times 10^5 \, \text{Pa} \]

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

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

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