Assertion:- A body may gain kinetic energy and potential energy simultaneously.
Reason:- Conservation of mechanical energy may not be valid every time.

Options

A. Only when no external forceacts on the system
B. Only when the objects move along closed path
C. Only when the work done by the resultant external force is zero
D. Only when the objects move under the action of a conservative force

Answer

To solve the assertion-reason question, we will analyze both the assertion and the reason step by step.

### Step 1: Analyze the Assertion
- **Assertion:** A body may gain kinetic energy and potential energy simultaneously.
- **Explanation:** Consider a body being lifted vertically against the force of gravity. As the body moves upward, it is acted upon by an external force (e.g., a person lifting it).
- As the body moves upward, its velocity increases due to the applied force, which means its kinetic energy (KE) is increasing. The formula for kinetic energy is:
\[ KE = \frac{1}{2} mv^2 \]
where \( m \) is the mass and \( v \) is the velocity of the body.
- Simultaneously, as the body moves higher, its height \( h \) increases, leading to an increase in gravitational potential energy (PE). The formula for potential energy is:
\[ PE = mgh \]
where \( g \) is the acceleration due to gravity.
- Therefore, both kinetic energy and potential energy can increase at the same time when a force is applied to lift the body.

### Step 2: Analyze the Reason
- **Reason:** Conservation of mechanical energy may not be valid every time.
- **Explanation:** The principle of conservation of mechanical energy states that in a closed system with only conservative forces acting (like gravity), the total mechanical energy (sum of kinetic and potential energy) remains constant. However:
- When an external force (like the lifting force) is applied, it does work on the system, adding energy to it. This means that the mechanical energy is not conserved because the external force does not fall under conservative forces.
- Therefore, in this scenario, the mechanical energy is not conserved, allowing both kinetic and potential energy to increase simultaneously.

### Conclusion
- Since both the assertion and the reason are correct and the reason provides a valid explanation for the assertion, we conclude that:
- **Both Assertion and Reason are correct, and the Reason is the correct explanation for the Assertion.**