Assertion: When percentage error in the meansurement of mass and velocity are `1%` and `2%` respectively the percentagwe error in K.E. is `5%`.
Reason: `(Delta K)/(K) = (Delta m)/(m) = (2 Delta v )/(v)`.

Options

A. if both assertion and reason are true reason is the correct explanation of assertion.
B. If both assertion and reason are true but reason is not the correct explanation fo assertion.
C. If assertion is true but reaso is false.
D. IF both assertion and reason are false.

Explanation

To solve the question, we need to analyze both the assertion and the reason provided in the question.

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

### Step 2: Finding the Percentage Error in K.E.
To find the percentage error in kinetic energy, we can use the formula for the percentage error in a product or a function of variables. The percentage error in kinetic energy can be expressed as:
\[ \frac{\Delta K.E.}{K.E.} = \frac{\Delta m}{m} + 2 \frac{\Delta v}{v} \]
where \( \Delta m \) is the absolute error in mass and \( \Delta v \) is the absolute error in velocity.

### Step 3: Substituting the Given Values
According to the problem, the percentage error in mass is \( 1\% \) and in velocity is \( 2\% \). We can substitute these values into the equation:
- \( \frac{\Delta m}{m} = 0.01 \) (1%)
- \( \frac{\Delta v}{v} = 0.02 \) (2%)

Now, substituting these into the equation:
\[ \frac{\Delta K.E.}{K.E.} = 0.01 + 2 \times 0.02 \]

### Step 4: Calculating the Total Percentage Error
Now we calculate:
\[ \frac{\Delta K.E.}{K.E.} = 0.01 + 0.04 = 0.05 \]
Converting this to percentage:
\[ \frac{\Delta K.E.}{K.E.} \times 100 = 0.05 \times 100 = 5\% \]

### Conclusion on the Assertion
The assertion states that the percentage error in K.E. is \( 5\% \), which we have calculated to be true.

### Step 5: Analyzing the Reason
The reason provided is:
\[ \frac{\Delta K}{K} = \frac{\Delta m}{m} = 2 \frac{\Delta v}{v} \]
This statement is incorrect because the correct relationship is:
\[ \frac{\Delta K}{K} = \frac{\Delta m}{m} + 2 \frac{\Delta v}{v} \]
Thus, the reason is false.

### Final Answer
- **Assertion**: True
- **Reason**: False