Assertion: Energy can not be given to a system without giving it momentum.
Reason: If kinetic energy is given to a body it means it has acquired momentum.

Options

A. (a) If both Assertion and Reason are true and the Reason is correct explanation of the Assertion.
B. (b) If both Assertion and Reason are true but Reason is not the correct explanation of Assertion.
C. (c) If Assertion is true, but the Reason is false.
D. (d) If Assertion is false but the Reason is true.

Explanation

To analyze the assertion and reason provided in the question, we will break down the concepts of energy, momentum, and their relationship step by step.

### Step-by-Step Solution:

1. **Understanding the Assertion**:
- The assertion states that "Energy cannot be given to a system without giving it momentum."
- This implies that whenever energy is added to a system, the system must also gain momentum.

2. **Analyzing the Reason**:
- The reason states that "If kinetic energy is given to a body, it means it has acquired momentum."
- This suggests that adding kinetic energy to a body results in the body gaining momentum.

3. **Consider a System**:
- Let's consider a system that consists of two masses (m1 and m2) which are initially at rest.
- If this system splits into two parts due to internal forces, the total momentum of the system before the split is zero.

4. **Applying Conservation of Momentum**:
- After the split, let m1 move with velocity v1 and m2 with velocity v2.
- By conservation of momentum, we have:
\[ m1 \cdot v1 + m2 \cdot v2 = 0 \]
- This means that the momentum of one mass is equal and opposite to the momentum of the other mass.

5. **Calculating Kinetic Energy**:
- The kinetic energy (KE) of the system can be calculated as:
\[ KE = \frac{1}{2} m1 v1^2 + \frac{1}{2} m2 v2^2 \]
- Even though the total momentum of the system is zero, the kinetic energy can still be greater than zero if both masses are moving.

6. **Conclusion on the Assertion**:
- Since we can have a situation where kinetic energy is present but the total momentum of the system is zero, the assertion is **false**.

7. **Conclusion on the Reason**:
- For a single body, if it gains kinetic energy, it indeed acquires momentum.
- The relationship between kinetic energy (KE) and momentum (P) for a body is given by:
\[ KE = \frac{P^2}{2m} \]
- Thus, if kinetic energy is greater than zero, momentum must also be greater than zero. Therefore, the reason is **true**.

8. **Final Answer**:
- The assertion is false, but the reason is true. Hence, the correct option is that the assertion is false and the reason is true.