Read the given statements and select the correct option.
Statement 1: If a light body and a heavy body possess the same kinetic energy, then the heavy body will possess more momentum.
Statement 2: Work done by all the forces on a body is equal to change in its kinetic energy.

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.

Answer

To solve the question, we need to analyze both statements provided.

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

- Kinetic energy (KE) is given by the formula:
\[ KE = \frac{1}{2}mv^2 \]
where \( m \) is mass and \( v \) is velocity.

- Momentum (p) is given by the formula:
\[ p = mv \]

- If both bodies have the same kinetic energy, we can set the kinetic energy equations equal to each other:
\[ \frac{1}{2}m_1v_1^2 = \frac{1}{2}m_2v_2^2 \]
where \( m_1 \) is the mass of the light body and \( m_2 \) is the mass of the heavy body.

- Rearranging gives:
\[ m_1v_1^2 = m_2v_2^2 \]

- From this, we can express the velocities in terms of kinetic energy:
\[ v_1 = \sqrt{\frac{2KE}{m_1}} \quad \text{and} \quad v_2 = \sqrt{\frac{2KE}{m_2}} \]

- Now, substituting these velocities into the momentum formula:
\[ p_1 = m_1v_1 = m_1\sqrt{\frac{2KE}{m_1}} = \sqrt{2m_1KE} \]
\[ p_2 = m_2v_2 = m_2\sqrt{\frac{2KE}{m_2}} = \sqrt{2m_2KE} \]

- Since \( m_2 > m_1 \) and both have the same kinetic energy, it follows that:
\[ p_2 > p_1 \]
- Therefore, Statement 1 is **true**.

### Step 2: Analyze Statement 2
**Statement 2:** Work done by all the forces on a body is equal to the change in its kinetic energy.

- This statement is a direct reference to the Work-Energy Theorem, which states that the work done on an object is equal to the change in its kinetic energy.
- Mathematically, it can be expressed as:
\[ W = \Delta KE = KE_{final} - KE_{initial} \]
- Therefore, Statement 2 is also **true**.

### Conclusion
Both statements are true. However, Statement 2 does not explain Statement 1; they are independent truths.

### Final Answer
Both statements are true, but Statement 2 is not a correct explanation of Statement 1.

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