A : The potential energy of a system increases when work is done by conservative force.
R : Kinetic energy can change into potential energy and vice-versa.

Options

A. If both Assertion & Reason are true and the reason is the correct explanation of the assertion, then mark (1).
B. If both Assertion & Reason are true but the reason is not the correct explanation of the assertion, then mark (2).
C. If Assertion is true statement but Reason is false, then mark (3).
D. If both Assertion and Reason are falsė statements, then mark (4).

Answer

To analyze the given statements, we need to evaluate both the assertion (A) and the reason (R) separately.

### Step 1: Evaluate the Assertion (A)
The assertion states: "The potential energy of a system increases when work is done by a conservative force."

1. **Understanding Conservative Forces**: A conservative force is one where the work done by the force on an object moving between two points is independent of the path taken. The work done by a conservative force is stored as potential energy.

2. **Example with Gravitational Force**: Consider the gravitational force, which is a classic example of a conservative force. When an object is lifted against gravity, work is done on the object.

3. **Calculating Work Done**: The work done (W) when lifting an object of mass (m) to a height (h) is given by:
\[ W = mgh \]
This work done is stored as gravitational potential energy (U):
\[ U = mgh \]

4. **Conclusion**: Since the potential energy increases as work is done against the gravitational force, the assertion is **True**.

### Step 2: Evaluate the Reason (R)
The reason states: "Kinetic energy can change into potential energy and vice-versa."

1. **Understanding Energy Transformation**: Kinetic energy (KE) is the energy of an object due to its motion, given by:
\[ KE = \frac{1}{2}mv^2 \]
Potential energy (PE) is the energy stored in an object due to its position in a force field (like gravitational).

2. **Energy Conversion**: In a closed system, kinetic energy can be converted into potential energy and vice versa. For example, when an object is thrown upwards, its kinetic energy decreases while its potential energy increases until it reaches its highest point, where kinetic energy is minimum and potential energy is maximum.

3. **Conclusion**: The statement about kinetic energy changing into potential energy and vice versa is also **True**.

### Step 3: Relationship Between Assertion and Reason
While both statements are true, we need to determine if the reason correctly explains the assertion.

1. **Explanation Check**: The assertion is about how potential energy increases due to work done by a conservative force. The reason discusses the transformation of kinetic energy to potential energy, which does not directly explain why potential energy increases when work is done by a conservative force.

2. **Final Conclusion**: The reason does not correctly explain the assertion, even though both are true. Thus, the correct relationship is that both A and R are true, but R does not explain A.

### Final Answer
- Assertion (A) is True.
- Reason (R) is True, but R does not explain A.