Read the given statements and select the correct option.
Statement 1: If a light body and a heavy body possess the same momentum, the lighter body will possess more kinetic energy.
Statement 2 : The kinetic energy of a body varies as the square of its velocity.

Options

A. Both statements 1 and 2 are true and statement 2 is the correct explanation of statement 1.
B. Both statements 1 and 2 are true but statement 2 is not the correct explanation of statement 1.
C. Statement 1 is true but statement 2 is false.
D. Both statements 1 and 2 are false.

Explanation

To solve the question, we need to analyze both statements provided and determine their correctness.

### Step 1: Analyze Statement 1
**Statement 1**: If a light body and a heavy body possess the same momentum, the lighter body will possess more kinetic energy.

- **Momentum (p)** is defined as the product of mass (m) and velocity (v):
\[ p = mv \]
- If two bodies (one light and one heavy) have the same momentum, we can express their velocities in terms of their masses:
\[ v_{\text{light}} = \frac{p}{m_{\text{light}}} \quad \text{and} \quad v_{\text{heavy}} = \frac{p}{m_{\text{heavy}}} \]
- Since \(m_{\text{light}} < m_{\text{heavy}}\), it follows that:
\[ v_{\text{light}} > v_{\text{heavy}} \]

### Step 2: Calculate Kinetic Energy
**Kinetic Energy (KE)** is given by the formula:
\[ KE = \frac{1}{2} mv^2 \]
- For the light body:
\[ KE_{\text{light}} = \frac{1}{2} m_{\text{light}} \left(\frac{p}{m_{\text{light}}}\right)^2 = \frac{p^2}{2m_{\text{light}}} \]
- For the heavy body:
\[ KE_{\text{heavy}} = \frac{1}{2} m_{\text{heavy}} \left(\frac{p}{m_{\text{heavy}}}\right)^2 = \frac{p^2}{2m_{\text{heavy}}} \]

### Step 3: Compare Kinetic Energies
- Since \(m_{\text{light}} < m_{\text{heavy}}\), we can see that:
\[ KE_{\text{light}} = \frac{p^2}{2m_{\text{light}}} > KE_{\text{heavy}} = \frac{p^2}{2m_{\text{heavy}}} \]
- Therefore, the lighter body indeed possesses more kinetic energy than the heavier body when both have the same momentum.

### Conclusion for Statement 1
**Statement 1 is true.**

### Step 4: Analyze Statement 2
**Statement 2**: The kinetic energy of a body varies as the square of its velocity.

- From the kinetic energy formula:
\[ KE = \frac{1}{2} mv^2 \]
- This shows that kinetic energy is directly proportional to the square of the velocity (v):
\[ KE \propto v^2 \]
- Therefore, **Statement 2 is also true.**

### Final Conclusion
Both statements are true, but Statement 2 is not the correct explanation for Statement 1.

The correct option is:
**Both Statement 1 and Statement 2 are true, but Statement 2 is not the correct explanation of Statement 1.**