A body is undergoing non-uniform circular motion. Work done by radial force on the body is

Options

A. zero
B. positive
C. negative
D. none of these

Answer

To determine the work done by the radial force on a body undergoing non-uniform circular motion, we can follow these steps:

### Step 1: Understand the Forces Involved
In circular motion, there are typically two types of forces acting on the body:
1. **Radial Force (Centripetal Force)**: This force acts towards the center of the circular path.
2. **Tangential Force**: This force acts along the direction of motion and is responsible for changing the speed of the body.

### Step 2: Identify the Direction of the Radial Force
The radial force always points towards the center of the circular path. Regardless of the position of the body on the circular path, the radial force remains directed inward.

### Step 3: Determine the Direction of Displacement
As the body moves along the circular path, its displacement at any point is tangential to the circle. This means that at any instant, the displacement vector is perpendicular to the radial force vector.

### Step 4: Analyze the Angle Between Radial Force and Displacement
Since the radial force is directed towards the center and the displacement is tangential, the angle between the radial force and the displacement is 90 degrees.

### Step 5: Calculate the Work Done
The work done (W) by a force is given by the formula:
\[ W = F \cdot d \cdot \cos(\theta) \]
where:
- \( F \) is the force,
- \( d \) is the displacement,
- \( \theta \) is the angle between the force and the displacement.

In this case:
- \( F \) is the radial force,
- \( d \) is the displacement,
- \( \theta = 90^\circ \).

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

### Step 6: Conclusion
Thus, the work done by the radial force on the body undergoing non-uniform circular motion is **0**.

### Final Answer
The work done by the radial force on the body is **0**.

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