Which of the following is/are true regarding work ?

Options

A. A force does positive work on the body if its kinetic energy is increasing.
B. A force can do zero work even if the kinetic energy of the body is changing.
C. A force can do negative work even if the kinetic energy of the body is increasing.
D. A force does positive work if the angle between the force vector and the displacement vector is acute.

Answer

To determine which statements regarding work are true, we will analyze each option based on the principles of physics, specifically the Work-Energy Theorem and the definition of work.

### Step-by-Step Solution:

1. **Understanding Work**:
Work is defined as the product of the force applied to an object and the displacement of that object in the direction of the force. Mathematically, it is represented as:
\[ W = F \cdot S = F \cdot S \cdot \cos(\theta) \]
where \( \theta \) is the angle between the force vector and the displacement vector.

2. **Analyzing the First Option**:
"A force does positive work on the body if its kinetic energy is increasing."
- If a force is acting in the same direction as the displacement, the work done is positive, which can lead to an increase in kinetic energy.
- **Conclusion**: This statement is **true**.

3. **Analyzing the Second Option**:
"A force can do zero work if the kinetic energy of the body is changing."
- Consider a scenario where an object moves in a circular path. The tension in the string acts perpendicular to the displacement, resulting in zero work done (since \( \cos(90^\circ) = 0 \)), while the kinetic energy can change due to the centripetal acceleration.
- **Conclusion**: This statement is **true**.

4. **Analyzing the Third Option**:
"A force can do negative work even if the kinetic energy of the body is increasing."
- For example, if an object is moving down an inclined plane with friction, the friction force does negative work (opposite to the direction of motion), but the gravitational force can still increase the kinetic energy of the object.
- **Conclusion**: This statement is **true**.

5. **Analyzing the Fourth Option**:
"A force does positive work if the angle between the force vector and the displacement vector is acute."
- When the angle \( \theta \) is acute (less than 90 degrees), \( \cos(\theta) \) is positive, leading to positive work being done.
- **Conclusion**: This statement is **true**.

6. **Final Conclusion**:
Since all the options provided are true regarding the concept of work, we can conclude that **all statements are correct**.

### Summary of Options:
- Option A: True
- Option B: True
- Option C: True
- Option D: True