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. `12%`
B. `10%`
C. `8%`
D. `2%`

Explanation

To find the percentage error in the measurement of kinetic energy (KE) 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 kinetic energy (KE) is given by the formula:
\[ KE = \frac{1}{2} mv^2 \]
where \( m \) is mass and \( v \) is speed.

2. **Identify the percentage errors**:
We are given:
- Percentage error in mass (\( \Delta m \)) = 2%
- Percentage error in speed (\( \Delta v \)) = 3%

3. **Determine the relationship between errors**:
The percentage error in kinetic energy can be calculated using the formula for the propagation of errors. For the kinetic energy formula, we have:
\[ \frac{\Delta KE}{KE} \times 100 = \frac{\Delta m}{m} \times 100 + 2 \times \frac{\Delta v}{v} \times 100 \]
Here, the factor of 2 comes from the fact that speed \( v \) is squared in the kinetic energy formula.

4. **Substitute the known percentage errors**:
Plugging in the values:
- For mass: \( \frac{\Delta m}{m} \times 100 = 2\% \)
- For speed: \( \frac{\Delta v}{v} \times 100 = 3\% \)

Therefore, the equation becomes:
\[ \frac{\Delta KE}{KE} \times 100 = 2\% + 2 \times 3\% \]

5. **Calculate the total percentage error**:
\[ \frac{\Delta KE}{KE} \times 100 = 2\% + 6\% = 8\% \]

6. **Conclusion**:
The percentage error in the measurement of kinetic energy is:
\[ \text{Percentage error in KE} = 8\% \]

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