A disc of radius `R` and mass `m` is projected on to a horizontal floor with a backward spin such that its centre of mass speed is `v_(0)` and angular velocity is `omega_(0)`. What must be the minimum value of `omega_(0)` so that the disc eventually returns back?

Explanation

To solve the problem, we need to determine the minimum value of the angular velocity \( \omega_0 \) such that the disc, projected with a backward spin, eventually returns back after sliding on the horizontal floor.

### Step-by-Step Solution:

1. **Understanding the Motion**:
- The disc is projected with a center of mass speed \( v_0 \) and an angular velocity \( \omega_0 \) in the backward direction. This means the translational motion is in one direction while the spin is in the opposite direction.

2. **Friction Force**:
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