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

Options

A. 0.08
B. 0.02
C. 0.12
D. 0.1

Explanation

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

### Step-by-Step Solution:

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

2. **Identify the percentage errors**:
- 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. **Express the percentage error in Kinetic Energy**:
The formula for the percentage error in kinetic energy can be derived from the formula for kinetic energy:
\[ \text{Percentage error in KE} = \frac{\Delta m}{m} + 2 \times \frac{\Delta v}{v} \]
Here, the term \( 2 \times \frac{\Delta v}{v} \) arises because speed is squared in the kinetic energy formula.

4. **Substitute the values of the percentage errors**:
- Convert the percentage errors into decimal form:
\[ \frac{\Delta m}{m} = \frac{2}{100} = 0.02 \]
\[ \frac{\Delta v}{v} = \frac{3}{100} = 0.03 \]

5. **Calculate the total percentage error in KE**:
Substitute the values into the formula:
\[ \text{Percentage error in KE} = 0.02 + 2 \times 0.03 \]
\[ = 0.02 + 0.06 = 0.08 \]

6. **Convert the result back to percentage**:
Since we calculated the error in decimal form, to express it as a percentage:
\[ \text{Percentage error in KE} = 0.08 \times 100 = 8\% \]

### Final Answer:
The error in the estimation of kinetic energy is **8%**.