The percentage errors in the measurement of mass and speed of a body are 2% and 3% respectively. What is the percentage error in the kinetic energy obtained by measuring its mass and speed?

Options

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

Explanation

To solve the problem of finding the percentage error in 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 kinetic energy (K) of a body is given by the formula:
\[ K = \frac{1}{2} mv^2 \]
where \(m\) is the mass and \(v\) is the speed of the body.

2. **Identify the Given Percentage Errors**:
- The percentage error in mass (\(m\)) is given as 2%.
- The percentage error in speed (\(v\)) is given as 3%.

3. **Determine the Formula for Percentage Error in Kinetic Energy**:
The percentage error in a product or quotient can be calculated using the following rule:
\[ \text{Percentage Error in } K = \text{Percentage Error in } m + 2 \times \text{Percentage Error in } v \]
This is because speed \(v\) is squared in the kinetic energy formula.

4. **Substitute the Given Values into the Formula**:
- Percentage error in mass (\(m\)): 2%
- Percentage error in speed (\(v\)): 3%
\[ \text{Percentage Error in } K = 2\% + 2 \times 3\% \]

5. **Calculate the Percentage Error**:
\[ \text{Percentage Error in } K = 2\% + 6\% = 8\% \]

6. **Conclusion**:
The percentage error in the kinetic energy obtained by measuring its mass and speed is **8%**.

### Final Answer:
The percentage error in kinetic energy is **8%**.

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