Assertion : In spring block system if length of spring and mass of block both are halved, then angular frequency of oscillations will remain unchanged.
Reason : Angular frequency is given by `omega = sqrt((k)/(m))` .

Options

A. If both Assertion and Reason are true and the Reason is correct explanation of the Assertion.
B. If both Assertion and Reason are true but Reason is not the correct explanation of Assertion.
C. If Assertion is true, but the Reason is false.
D. If Assertion is false but the Reason is true.

Explanation

To solve the question, we need to analyze both the assertion and the reason provided.

### Step-by-Step Solution:

1. **Understanding the Assertion**:
The assertion states that if the length of the spring and the mass of the block are both halved, the angular frequency of oscillations will remain unchanged.

2. **Understanding the Reason**:
The reason provided states that the angular frequency (ω) is given by the formula:
\[ \omega = \sqrt{\frac{k}{m}} \]
where \( k \) is the spring constant and \( m \) is the mass of the block.

3. **Analyzing the Effect of Halving the Mass**:
If the mass \( m \) is halved, we have:
\[ m' = \frac{m}{2} \]

4. **Analyzing the Effect of Halving the Length of the Spring**:
The spring constant \( k \) is inversely proportional to the length of the spring. If the length \( L \) is halved, the new spring constant \( k' \) will be:
\[ k' = 2k \]
(because \( k \propto \frac{1}{L} \))

5. **Calculating the New Angular Frequency**:
Now, substituting \( k' \) and \( m' \) into the angular frequency formula:
\[ \omega' = \sqrt{\frac{k'}{m'}} = \sqrt{\frac{2k}{\frac{m}{2}}} = \sqrt{\frac{2k \cdot 2}{m}} = \sqrt{\frac{4k}{m}} = 2\sqrt{\frac{k}{m}} = 2\omega \]
This shows that the new angular frequency \( \omega' \) is actually twice the original angular frequency \( \omega \).

6. **Conclusion**:
Since the new angular frequency is \( 2\omega \), the assertion that the angular frequency remains unchanged is incorrect. However, the reason provided about the formula for angular frequency is correct.

### Final Answer:
- **Assertion**: Incorrect
- **Reason**: Correct