A circular racetrack of radius 100 m is banked at an angle of `45^(@)`. What is the
(i) Optimum speed of race car to avoid wear and tear of its tyres?
(ii) Maximum permissible speed to avoid slipping if the coefficient of friction is 0.2?

Explanation

To solve the problem, we will break it down into two parts:

### Part (i): Optimum Speed of the Race Car

1. **Identify the given values**:
- Radius of the track, \( R = 100 \, \text{m} \)
- Angle of banking, \( \theta = 45^\circ \)
- Acceleration due to gravity, \( g = 9.8 \, \text{m/s}^2 \)
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