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The image presents the following problem:

"While measuring \( g \) using the simple pendulum method, the percentage error in the measurement of length is ±2%, and in the measurement of time is ±3%. Calculate the relative error in \( g \)."

### Solution:

The formula for \( g \) using the simple pendulum method is:

\[
g = \frac{4 \pi^2 L}{T^2}
\]

Where:
- \( L \) is the length of the pendulum,
- \( T \) is the time period.

To find the relative error in \( g \), we use the rules for propagation of errors in multiplication and powers.

#### Error Propagation Rule:
1. When quantities are multiplied or divided, the relative errors add.
2. When a quantity is raised to a power, the relative error is multiplied by the absolute value of the exponent.

The relative error in \( g \), \( \frac{\Delta g}{g} \), is given by the following formula:

\[
\frac{\Delta g}{g} = \frac{\Delta L}{L} + 2 \times \frac{\Delta T}{T}
\]

Given:
- The percentage error in length \( \frac{\Delta L}{L} = 2\% \),
- The percentage error in time \( \frac{\Delta T}{T} = 3\% \).

Substituting these values:

\[
\frac{\Delta g}{g} = 2\% + 2 \times 3\%
\]

\[
\frac{\Delta g}{g} = 2\% + 6\% = 8\%
\]

Thus, the relative error in \( g \) is **8%**.

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Would you like more details, or do you have any further questions?

Here are some related questions you might consider:
1. What is the significance of error propagation in experimental physics?
2. How does the formula for the period of a pendulum relate to gravity?
3. How does increasing the length of the pendulum affect the percentage error in \( g \)?
4. Can you calculate the absolute error in \( g \) if its value was given as \( 9.8 \, \text{m/s}^2 \)?
5. How does the square of the time period affect the overall calculation of the relative error?

**Tip:** Remember, when dealing with powers in error propagation, multiply the error by the power's exponent.

While measuring g using simple pendulum method, percentage error in measurement of length is ±2% and in measurement of time is ±3%. Calculate relative error in g.

Learn how to calculate the relative error in g using the simple pendulum method. This problem involves error propagation, and it covers percentage error in length and time. Ideal for students in Grades 11-12 studying error analysis in physics.

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