Choose the incorrect statement.

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 non-conservative.
D. All the central forces are non-conservative.

Answer

To solve the question, we need to analyze each statement provided in the options and determine which one is incorrect. Let's go through the options step by step:

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

**Explanation:**
- Work done (W) is calculated using the formula:
\[ W = F \cdot d \cdot \cos(\theta) \]
where \(F\) is the force applied, \(d\) is the displacement, and \(\theta\) is the angle between the force and displacement vectors.
- If the displacement is perpendicular to the force, then \(\theta = 90^\circ\).
- Therefore, \(\cos(90^\circ) = 0\), which means:
\[ W = F \cdot d \cdot 0 = 0 \]
- **Conclusion:** This statement is correct.

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

**Explanation:**
- An obtuse angle means \(\theta > 90^\circ\).
- In this case, \(\cos(\theta)\) will be negative.
- Thus, the work done becomes:
\[ W = F \cdot d \cdot \cos(\theta) < 0 \]
- **Conclusion:** This statement is also correct.

### Step 3: Analyze Option C
**Statement:** Frictional force is non-conservative.

**Explanation:**
- A non-conservative force is one for which the work done depends on the path taken. Frictional force is a classic example of a non-conservative force.
- If a body moves in a closed path, the work done by friction is not zero, indicating that it dissipates energy.
- **Conclusion:** This statement is correct.

### Step 4: Analyze Option D
**Statement:** All central forces are non-conservative.

**Explanation:**
- Central forces, such as gravitational and electrostatic forces, are conservative forces. They depend only on the distance from the center and not on the path taken.
- For example, the work done by gravitational force in moving an object from one point to another is independent of the path taken.
- **Conclusion:** This statement is incorrect.

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

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