Which of the following statements is incorrect?

Options

A. No work is done if the displacement is perpendicular to the direction of the applied force.
B. If the angle between the force and displacement Vectors is obtuse, then the work done is negative
C. Frictional force is a non-conservative
D. All the central forces are non-conservative

Explanation

To determine which statement is incorrect, we will analyze each statement one by one.

### Step 1: Analyze the First Statement
**Statement:** No work is done if the displacement is perpendicular to the direction of the applied force.

- **Explanation:** Work done (W) is calculated using the formula:
\[ W = F \cdot d \cdot \cos(\theta) \]
where \(F\) is the force, \(d\) is the displacement, and \(\theta\) is the angle between the force and displacement vectors. If the displacement is perpendicular to the force, then \(\theta = 90^\circ\).

- **Calculation:**
\[ W = F \cdot d \cdot \cos(90^\circ) = F \cdot d \cdot 0 = 0 \]

- **Conclusion:** This statement is true.

### Step 2: Analyze the Second Statement
**Statement:** If the angle between the force and displacement vector is obtuse, then the work done is negative.

- **Explanation:** An obtuse angle is greater than \(90^\circ\) and less than \(180^\circ\). In this case, \(\cos(\theta)\) will be negative.

- **Calculation:** For example, if \(\theta = 120^\circ\):
\[ W = F \cdot d \cdot \cos(120^\circ) = F \cdot d \cdot (-0.5) = -\frac{F \cdot d}{2} \]

- **Conclusion:** This statement is true.

### Step 3: Analyze the Third Statement
**Statement:** Frictional force is a non-conservative force.

- **Explanation:** Non-conservative forces are those that depend on the path taken. Friction is a classic example of a non-conservative force because the work done against friction depends on the distance traveled.

- **Conclusion:** This statement is true.

### Step 4: Analyze the Fourth Statement
**Statement:** All central forces are non-conservative.

- **Explanation:** Central forces, such as gravitational and electrostatic forces, depend only on the positions of the objects and not on the path taken. Therefore, they are conservative forces.

- **Conclusion:** This statement is false.

### Final Conclusion
The incorrect statement is:
**"All central forces are non-conservative."**