A tangential force F is applied on a disc of radius R, due to which it deflects through an angle `theta` from its initial position. The work done by this force would be

Options

A. FR
B. `Ftheta`
C. `(FR)/(theta)`
D. `FR theta`

Answer

To solve the problem of calculating the work done by a tangential force \( F \) applied to a disc of radius \( R \) that deflects through an angle \( \theta \), we can follow these steps:

### Step-by-Step Solution:

1. **Understanding the Setup**:
- We have a disc of radius \( R \) that is initially at rest.
- A tangential force \( F \) is applied at the edge of the disc, causing it to rotate about its center.

2. **Identifying the Torque**:
- The torque \( \tau \) generated by the tangential force \( F \) can be calculated using the formula:
\[ \tau = R \times F \]
- Here, \( R \) is the radius of the disc, and \( F \) is the tangential force applied.

3. **Relating Torque to Angular Displacement**:
- The work done \( W \) in rotational motion can be expressed in terms of torque and angular displacement:
\[ W = \tau \times \theta \]
- Where \( \theta \) is the angular displacement in radians.

4. **Substituting Torque into the Work Done Formula**:
- Now, substituting the expression for torque into the work done formula:
\[ W = (R \times F) \times \theta \]
- This simplifies to:
\[ W = F \times R \times \theta \]

5. **Final Expression for Work Done**:
- Therefore, the work done by the tangential force \( F \) when the disc deflects through an angle \( \theta \) is:
\[ W = F R \theta \]

### Conclusion:
The work done by the tangential force \( F \) on the disc is given by the formula:
\[ W = F R \theta \]