A solid disc and a ring, both of radius `10 cm` are placed on a horizontal table simultaneously, with initial angular speed equal to `10 pi rad//s`. Which of the two will start to roll earlier ? The coefficient of kinetic friction is `mu_(k) = 0.2`.

Explanation

To solve the problem of determining which object, a solid disc or a ring, will start to roll earlier when both are placed on a horizontal table with an initial angular speed of \(10\pi\) rad/s, we need to analyze the motion of both objects under the influence of kinetic friction.

### Step-by-Step Solution:

1. **Identify Given Data:**
- Radius of both the disc and the ring, \( R = 10 \, \text{cm} = 0.1 \, \text{m} \)
- Initial angular speed, \( \omega_0 = 10\pi \, \text{rad/s} \)
- Coefficient of kinetic friction, \( \mu_k = 0.2 \)
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