Will the ring roll purely if force `F` is applied in between topmost point and centre and the surface is smooth.

Explanation

To determine whether the ring will roll purely when a force \( F \) is applied between the topmost point and the center of the ring on a smooth surface, we can analyze the situation step by step.

### Step-by-Step Solution:

1. **Understanding the Setup**:
- We have a ring with radius \( R \).
- A force \( F \) is applied at a point between the topmost point of the ring and its center.

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