The percentage error in measurements of length and time period is `2%` and `1%` respectively . The percentage error in measurements of 'g' is

Options

A. `2%`
B. `4%`
C. `6%`
D. `8%`

Answer

To find the percentage error in the measurement of 'g', we need to consider the formula for 'g' and how the errors in its constituent measurements contribute to the overall error.

### Step-by-Step Solution:

1. **Understand the formula for 'g':**
The acceleration due to gravity 'g' can be expressed in terms of length (L) and time (T) as:
\[ g = \frac{L}{T^2} \]
where L is the length and T is the time period.

2. **Identify the percentage errors:**
We are given:
- Percentage error in length (L) = 2%
- Percentage error in time period (T) = 1%

3. **Determine the contribution of each measurement to the error in 'g':**
The formula for the percentage error in a quotient or product is given by:
\[ \text{Percentage error in } g = \text{Percentage error in } L + 2 \times \text{Percentage error in } T \]
Here, we multiply the percentage error in time (1%) by 2 because time is squared in the formula for 'g'.

4. **Substitute the values:**
Now we can substitute the known values into the formula:
\[ \text{Percentage error in } g = 2\% + 2 \times 1\% \]
\[ = 2\% + 2\% \]
\[ = 4\% \]

5. **Conclusion:**
Therefore, the percentage error in the measurement of 'g' is:
\[ \boxed{4\%} \]