The percentage error in the measurement of mass and speed are 2% and 3% respectively. Maximum estimate of percentage error of K.E

Options

A. 0.11
B. 0.08
C. 0.05
D. 0.01

Answer

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

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

3. **Use the Rule for Maximum Percentage Error**:
The maximum percentage error in a product or power can be calculated using the following formula:
\[ \text{Percentage error in K.E} = \left( \frac{\Delta m}{m} + 2 \cdot \frac{\Delta v}{v} \right) \times 100 \]
Here, the speed \( v \) is squared in the kinetic energy formula, so its percentage error is multiplied by 2.

4. **Substitute the Values**:
Substitute the given percentage errors into the formula:
\[ \text{Percentage error in K.E} = \left( 2\% + 2 \cdot 3\% \right) \]
\[ = 2\% + 6\% = 8\% \]

5. **Convert to Decimal Form**:
To express the percentage error in decimal form:
\[ \text{Percentage error in K.E} = 8\% = 0.08 \]

6. **Conclusion**:
The maximum estimate of the percentage error in kinetic energy is \( 0.08 \).

### Final Answer:
The maximum estimate of the percentage error in kinetic energy is **0.08**.

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