Calculate percentage error in determination of time period of a pendulum.
`T = 2pi (sqrt(l))/(g)`
where, l and g are measured with `+-1%` and `+-2%`.

Explanation

To calculate the percentage error in the determination of the time period \( T \) of a pendulum, we start with the formula given:

\[ T = 2\pi \sqrt{\frac{l}{g}} \]

where \( l \) is the length of the pendulum and \( g \) is the acceleration due to gravity. The errors in the measurements of \( l \) and \( g \) are given as \( \pm 1\% \) and \( \pm 2\% \) respectively.

### Step 1: Identify the formula for percentage error

The formula for the percentage error in a function of multiple variables can be expressed as:

\[ \frac{\Delta T}{T} = \frac{1}{2} \frac{\Delta l}{l} + \frac{1}{2} \frac{\Delta g}{g} \]

where:
- \( \Delta T \) is the absolute error in \( T \)
- \( T \) is the measured value of the time period
- \( \Delta l \) is the absolute error in \( l \)
- \( l \) is the measured value of the length
- \( \Delta g \) is the absolute error in \( g \)
- \( g \) is the measured value of the acceleration due to gravity

### Step 2: Convert percentage errors to fractional errors

Given:
- The percentage error in \( l \) is \( \pm 1\% \), which means \( \frac{\Delta l}{l} = \frac{1}{100} = 0.01 \).
- The percentage error in \( g \) is \( \pm 2\% \), which means \( \frac{\Delta g}{g} = \frac{2}{100} = 0.02 \).

### Step 3: Substitute the fractional errors into the formula

Now substituting these values into the percentage error formula:

\[ \frac{\Delta T}{T} = \frac{1}{2} \cdot 0.01 + \frac{1}{2} \cdot 0.02 \]

### Step 4: Calculate the total percentage error

Calculating the right-hand side:

\[ \frac{\Delta T}{T} = \frac{1}{2} \cdot 0.01 + \frac{1}{2} \cdot 0.02 = 0.005 + 0.01 = 0.015 \]

### Step 5: Convert to percentage

To convert this to a percentage error, we multiply by 100:

\[ \text{Percentage Error in } T = 0.015 \times 100 = 1.5\% \]

### Final Result

Thus, the percentage error in the determination of the time period \( T \) of the pendulum is:

\[ \pm 1.5\% \]

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