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

### Step 1: Understand the formula for kinetic energy
The formula for kinetic energy (K.E.) is given by:
\[ K.E. = \frac{1}{2} mv^2 \]
where \( m \) is the mass and \( v \) is the speed.

### Step 2: Identify the percentage errors
The problem states that:
- The percentage error in the measurement of mass (\( m \)) is \( 2\% \).
- The percentage error in the measurement of speed (\( v \)) is \( 3\% \).

### Step 3: Use the formula for percentage error in kinetic energy
The percentage error in kinetic energy can be calculated using the formula:
\[ \text{Percentage error in } K.E. = \left(\frac{\Delta m}{m} \times 100\right) + 2 \left(\frac{\Delta v}{v} \times 100\right) \]
where \( \Delta m \) and \( \Delta v \) are the absolute errors in mass and speed, respectively.

### Step 4: Substitute the known values
Substituting the given percentage errors into the formula:
\[ \text{Percentage error in } K.E. = 2\% + 2 \times 3\% \]
Calculating this gives:
\[ \text{Percentage error in } K.E. = 2\% + 6\% = 8\% \]

### Step 5: Conclusion
Thus, the error in the measurement of kinetic energy is \( 8\% \).

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

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