Assertion: Energy associated with a mere kilogram of matter is `9 xx 10^16 J`
Reason: It follows from the relation `E = mc^2`.

Options

A. If both assertion and reason are true and reason is the correct explanation of assertion.
B. If both assertion and reason are true not but reason is not the correct explanation of assertion.
C. If assertion is true but reason 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.

### Step-by-Step Solution:

1. **Understanding the Assertion**:
The assertion states that the energy associated with a mere kilogram of matter is \(9 \times 10^{16} \, J\).

2. **Using Einstein's Equation**:
We will use Einstein's famous equation \(E = mc^2\) to verify the assertion. Here, \(E\) is the energy, \(m\) is the mass, and \(c\) is the speed of light in a vacuum.

3. **Substituting Values**:
For \(m = 1 \, kg\) (as stated in the assertion), and knowing that the speed of light \(c\) is approximately \(3 \times 10^8 \, m/s\), we can substitute these values into the equation:
\[ E = 1 \, kg \times (3 \times 10^8 \, m/s)^2 \]

4. **Calculating \(c^2\)**:
Now, we calculate \(c^2\):
\[ c^2 = (3 \times 10^8)^2 = 9 \times 10^{16} \, m^2/s^2 \]

5. **Calculating Energy \(E\)**:
Now substituting \(c^2\) back into the equation for energy:
\[ E = 1 \, kg \times 9 \times 10^{16} \, m^2/s^2 = 9 \times 10^{16} \, J \]

6. **Conclusion about the Assertion**:
The calculated energy \(E\) matches the assertion \(9 \times 10^{16} \, J\). Therefore, the assertion is true.

7. **Analyzing the Reason**:
The reason states that this energy follows from the relation \(E = mc^2\). Since we derived the assertion directly from this equation, the reason is also true and correctly explains the assertion.

8. **Final Answer**:
Both the assertion and the reason are true, and the reason is the correct explanation of the assertion.

### Answer:
Both assertion and reason are true, and the reason is the correct explanation of the assertion.

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