Statement-I: If error in measurement of mass is 2% and that in measurement of velocity is 5% than error in measurement of kinetic energy is 6%.
Statement -II: Error in kinetic energy is `(DeltaK)/(K) = ((Deltam)/(m)+2(Deltav)/(v))`

Options

A. Statement-1 is true and statement -2 is true
B. Statement -1 is true and statement-2 is false
C. Statement-1 is false and statement -2 is true
D. Statement-1 is false and statement -2 is false

Answer

To solve the problem, we need to analyze the two statements provided regarding the errors in measurements of mass and velocity, and how they relate to the error in kinetic energy.

### Step-by-Step Solution:

1. **Identify the Formula for Kinetic Energy**:
The formula for kinetic energy (K) is given by:
\[ K = \frac{1}{2} mv^2 \]

2. **Determine the Error in Kinetic Energy**:
To find the error in kinetic energy, we will use the formula for relative error in a product. The relative error in kinetic energy can be expressed as:
\[ \frac{\Delta K}{K} = \frac{\Delta m}{m} + 2\frac{\Delta v}{v} \]
where \(\Delta K\) is the absolute error in kinetic energy, \(K\) is the kinetic energy, \(\Delta m\) is the absolute error in mass, \(m\) is the mass, \(\Delta v\) is the absolute error in velocity, and \(v\) is the velocity.

3. **Substituting the Given Errors**:
According to the problem, the percentage error in mass (\(\frac{\Delta m}{m}\)) is 2%, and the percentage error in velocity (\(\frac{\Delta v}{v}\)) is 5%. We can substitute these values into the error formula:
\[ \frac{\Delta K}{K} = 0.02 + 2 \times 0.05 \]

4. **Calculating the Total Error**:
Now, we calculate the total error:
\[ \frac{\Delta K}{K} = 0.02 + 0.10 = 0.12 \]
To express this as a percentage, we multiply by 100:
\[ \frac{\Delta K}{K} \times 100 = 0.12 \times 100 = 12\% \]

5. **Conclusion**:
The calculated error in kinetic energy is 12%, which contradicts Statement-I that claims the error is 6%. Therefore, Statement-I is incorrect, while Statement-II, which provides the correct formula for calculating the error in kinetic energy, is correct.

### Final Answer:
- Statement-I is incorrect.
- Statement-II is correct.