Assertion: In the relation`f = (1)/(2l) sqrt((T)/(m))`, where symbols have standard meaning , m represent linear mass density.
Reason: The frequency has the dimensions inverse of time.

Options

A. a. If both assertion and reason are ture and reason is the correct explanation of assertion
B. b. If both assertion and reason are true but reason is not the correct explanation of assertion
C. c. If assertion is true but reason is false
D. d. If both assertion and reson are false.

Explanation

To solve the given assertion and reason question, we need to analyze both the assertion and the reason step by step.

### Step 1: Understanding the Assertion
The assertion states that in the relation \( f = \frac{1}{2l} \sqrt{\frac{T}{m}} \), where \( m \) represents linear mass density. We need to verify if this relation is dimensionally correct.

### Step 2: Identifying the Dimensions
1. **Frequency (f)**: The dimension of frequency is given by:
\[ [f] = M^0 L^0 T^{-1} \]
This indicates that frequency has dimensions of inverse time.

2. **Tension (T)**: The dimension of tension is the same as that of force, which is:
\[ [T] = M^1 L^1 T^{-2} \]

3. **Linear Mass Density (m)**: Linear mass density is mass per unit length, so its dimension is:
\[ [m] = M^1 L^{-1} T^0 \]

### Step 3: Analyzing the Right-Hand Side (RHS)
Now, we need to analyze the RHS of the equation \( \frac{T}{m} \):
\[ \frac{T}{m} = \frac{M^1 L^1 T^{-2}}{M^1 L^{-1}} = M^{1-1} L^{1-(-1)} T^{-2} = M^0 L^{2} T^{-2} \]

Taking the square root of this expression:
\[ \sqrt{\frac{T}{m}} = \sqrt{M^0 L^{2} T^{-2}} = M^0 L^{1} T^{-1} \]

### Step 4: Analyzing the Full Expression
Now substituting back into the equation:
\[ f = \frac{1}{2l} \sqrt{\frac{T}{m}} = \frac{1}{2l} (M^0 L^1 T^{-1}) \]
Here, \( l \) (length) has the dimension:
\[ [l] = M^0 L^1 T^0 \]

Thus, the dimension of \( \frac{1}{2l} \) is:
\[ \frac{1}{l} = M^0 L^{-1} T^0 \]

Now multiplying:
\[ f = (M^0 L^{-1} T^0)(M^0 L^1 T^{-1}) = M^0 L^{0} T^{-1} \]

### Step 5: Conclusion for Assertion
The dimension of \( f \) is \( M^0 L^0 T^{-1} \), which matches the dimension of frequency. Therefore, the assertion is correct.

### Step 6: Analyzing the Reason
The reason states that the frequency has the dimensions of inverse time, which is indeed true:
\[ [f] = M^0 L^0 T^{-1} \]

### Final Conclusion
Both the assertion and the reason are correct, but the reason does not provide a complete explanation for the assertion. Therefore, the correct option is that the assertion is true, and the reason is true but not a correct explanation of the assertion.