Percentage error in the measurement of mass and speed are 2% and 3% respectively. The error in the measurement of kinetic energy obtained by measuring mass and speed will be

Options

A. 0.12
B. 0.1
C. 0.08
D. 0.05

Explanation

To find the percentage error in the measurement of kinetic energy based on the percentage errors in mass and speed, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Formula for Kinetic Energy**:
The formula for kinetic energy (KE) is given by:
\[ KE = \frac{1}{2} m v^2 \]

2. **Identify the Variables**:
- Let \( m \) be the mass.
- Let \( v \) be the speed.
- The percentage error in mass (\( \Delta m/m \)) is given as 2%.
- The percentage error in speed (\( \Delta v/v \)) is given as 3%.

3. **Determine the Error Formula**:
The percentage error in kinetic energy can be derived from the errors in mass and speed. The formula for the percentage error in kinetic energy is:
\[ \frac{\Delta KE}{KE} = \frac{\Delta m}{m} + 2 \frac{\Delta v}{v} \]
Here, the factor of 2 in front of the speed error is due to the fact that speed is squared in the kinetic energy formula.

4. **Substitute the Given Errors**:
Now, substituting the given percentage errors into the formula:
- Percentage error in mass = 2%
- Percentage error in speed = 3%
\[ \frac{\Delta KE}{KE} = \frac{2}{100} + 2 \times \frac{3}{100} \]

5. **Calculate the Total Percentage Error**:
\[ \frac{\Delta KE}{KE} = \frac{2}{100} + \frac{6}{100} = \frac{8}{100} \]
Thus, the percentage error in kinetic energy is:
\[ \Delta KE = 8\% \]

6. **Final Answer**:
Therefore, the error in the measurement of kinetic energy obtained by measuring mass and speed will be **8%**.