In the measurement of a physical quantity (L), the formula used is `L=k(m xx n)`, where k is a constant and m and n are the quantities to be measured. If the % errors in m and n are respectively 3% and 5%. The % error in the measurement of L is

Options

A. `2%`
B. `5%`
C. `8%`
D. `3%`

Answer

To find the percentage error in the measurement of the physical quantity \( L \) given by the formula \( L = k(m \times n) \), where \( k \) is a constant and \( m \) and \( n \) are the quantities being measured, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Formula**: The formula for \( L \) is given as:
\[ L = k \cdot (m \times n) \]
Here, \( k \) is a constant, and \( m \) and \( n \) are the quantities with their respective percentage errors.

2. **Identify the Percentage Errors**: The problem states that:
- The percentage error in \( m \) is \( 3\% \).
- The percentage error in \( n \) is \( 5\% \).

3. **Use the Rule for Multiplication**: When multiplying quantities, the percentage errors add up. Therefore, the total percentage error in \( L \) can be calculated as:
\[ \text{Percentage Error in } L = \text{Percentage Error in } m + \text{Percentage Error in } n \]

4. **Calculate the Total Percentage Error**:
\[ \text{Percentage Error in } L = 3\% + 5\% = 8\% \]

5. **Conclusion**: The percentage error in the measurement of \( L \) is:
\[ \boxed{8\%} \]