In the formula `T=2pisqrt((l)/(g)),T` is ____proportional to `sqrt(l)`.

Answer

To determine how \( T \) is related to \( \sqrt{l} \) in the formula \( T = 2\pi \sqrt{\frac{l}{g}} \), we can analyze the formula step by step.

### Step-by-Step Solution:

1. **Identify the Formula**:
We start with the given formula:
\[ T = 2\pi \sqrt{\frac{l}{g}} \]

2. **Simplify the Square Root**:
We can rewrite the square root term:
\[ T = 2\pi \cdot \frac{\sqrt{l}}{\sqrt{g}} \]

3. **Observe the Relationship**:
From the simplified formula, we can see that \( T \) is directly related to \( \sqrt{l} \). The term \( \frac{2\pi}{\sqrt{g}} \) is a constant multiplier.

4. **Conclusion**:
Since \( T \) is expressed as a constant multiplied by \( \sqrt{l} \), we can conclude that:
\[ T \text{ is directly proportional to } \sqrt{l} \]

### Final Answer:
Thus, in the formula \( T = 2\pi \sqrt{\frac{l}{g}} \), \( T \) is **directly proportional** to \( \sqrt{l} \).

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