To estimate `g` (from `g = 4 pi^(2)(L)/(T^(2))`), error in measurement of `L` is `+- 2%` and error in measurement of `Tis +- 3%` The error in estimated `g` will be

Options

A. `pm8%`
B. `pm 6%`
C. `pm 3%`
D. `pm5%`

Explanation

To estimate the error in the measurement of \( g \) from the formula \( g = \frac{4 \pi^2 L}{T^2} \), we need to consider the percentage errors in the measurements of \( L \) and \( T \).

### Step-by-Step Solution:

1. **Identify the formula for \( g \)**:
\[ g = \frac{4 \pi^2 L}{T^2} \]

2. **Determine the percentage error in \( g \)**:
The formula for the percentage error in a function of multiple variables can be expressed as:
\[ \frac{\Delta g}{g} \times 100 = \frac{\Delta L}{L} \times 100 + 2 \times \frac{\Delta T}{T} \times 100 \]
Here, \( \Delta L \) is the error in measurement of \( L \) and \( \Delta T \) is the error in measurement of \( T \).

3. **Substitute the given percentage errors**:
- The error in measurement of \( L \) is \( \pm 2\% \):
\[ \frac{\Delta L}{L} \times 100 = \pm 2\% \]
- The error in measurement of \( T \) is \( \pm 3\% \):
\[ \frac{\Delta T}{T} \times 100 = \pm 3\% \]

4. **Plug in the values into the error formula**:
\[ \frac{\Delta g}{g} \times 100 = \pm 2\% + 2 \times (\pm 3\%) \]
This simplifies to:
\[ \frac{\Delta g}{g} \times 100 = \pm 2\% + \pm 6\% \]

5. **Combine the errors**:
\[ \frac{\Delta g}{g} \times 100 = \pm 8\% \]

6. **Conclusion**:
The error in the estimated value of \( g \) is \( \pm 8\% \).

### Final Answer:
The error in the estimated \( g \) will be \( \pm 8\% \).