Select the correct option(s).

Options

A. (a) A single external force acting on a particle necessarily changes its momentum and kinetic energy.
B. (b) A single external force acting on a particle necessarily changes its momentum.
C. (c) The work-energy theorem is valid for all types of forces: internal, external, conservative as well as non-conservative.
D. (d) The kinetic energy of the system can be increased without applying any external force on the system.

Explanation

To solve the question, we need to analyze each of the given options regarding the effects of forces on momentum and kinetic energy. Let's break it down step by step.

### Step 1: Analyze the first option
The first option states that a single external force acting on a particle necessarily changes its momentum and kinetic energy.

- **Momentum**: Momentum is defined as the product of mass and velocity (p = mv). If a single external force acts on a particle, it will cause the particle to accelerate, which means the velocity will change. Therefore, the momentum will change.

- **Kinetic Energy**: Kinetic energy is given by the formula KE = (1/2)mv². While the force changes the velocity, it is possible for the speed to remain constant if the force is perpendicular to the velocity, such as in uniform circular motion. In this case, the kinetic energy does not change even though the momentum does.

**Conclusion**: The first option is **incorrect** because while the momentum changes, the kinetic energy may not.

### Step 2: Analyze the second option
The second option states that work-energy theorem is valid for all types of forces: internal, external, conservative, and non-conservative.

- The work-energy theorem states that the work done by all forces acting on a particle is equal to the change in its kinetic energy. This includes all types of forces.

- Internal forces can also do work and change the kinetic energy of a system. For example, in an explosion, internal forces can cause particles to gain velocity.

**Conclusion**: The second option is **correct**.

### Step 3: Analyze the third option
The third option states that the kinetic energy of a system can be increased without applying any external force.

- This can occur through internal forces. For instance, in the case of an explosion, the internal forces can do work on the particles, increasing their kinetic energy without any external force being applied.

**Conclusion**: The third option is **correct**.

### Final Conclusion
Based on the analysis:
- The first option is incorrect.
- The second option is correct.
- The third option is correct.

Thus, the correct options are **B and C**.

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