In Q.4. work done by tangential force on the body is

Options

A. zero
B. non-zero
C. sometimes zero and other times not
D. cannot say

Answer

To solve the question regarding the work done by the tangential force on a body, we will follow these steps:

### Step 1: Understand the Concept of Work Done
Work done (W) by a force is defined as the product of the force (F) and the displacement (d) in the direction of the force. Mathematically, it is given by:
\[ W = F \cdot d \cdot \cos(\theta) \]
where \( \theta \) is the angle between the force and the direction of displacement.

### Step 2: Identify the Forces Acting on the Body
In this scenario, we have two forces acting on the body:
- **Centripetal Force**: This force acts towards the center of the circular path and does not do any work because it is always perpendicular to the displacement of the body.
- **Tangential Force**: This force acts along the direction of motion (tangentially) and can do work on the body depending on the displacement.

### Step 3: Analyze the Work Done by Each Force
- **Work Done by Centripetal Force**: Since the centripetal force is always perpendicular to the displacement of the body, the work done by the centripetal force is zero:
\[ W_{\text{centripetal}} = 0 \]

- **Work Done by Tangential Force**: The tangential force does work as it acts in the direction of the displacement. Therefore, the work done by the tangential force can be expressed as:
\[ W_{\text{tangential}} = F_{\text{tangential}} \cdot d \cdot \cos(0) \]
Since the angle \( \theta = 0 \) (force and displacement are in the same direction), we have:
\[ W_{\text{tangential}} = F_{\text{tangential}} \cdot d \]

### Step 4: Conclusion
The work done by the tangential force is non-zero as long as there is a displacement in the direction of the force. Therefore, we conclude that the work done by the tangential force on the body is non-zero.

### Final Answer
The work done by the tangential force on the body is non-zero.

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