A circular racetrack of radius 300 m is banked at an angle of `15^(@)` If the coefficient of friction between the wheels of a race car and the road is 0.2 what is the (a) optimum speed of the race car to avoid wear and tear on its tyres , and (b) maximum permissible speed to aviod slipping ?

Explanation

To solve the problem step by step, we will break it down into two parts: (a) finding the optimum speed of the race car to avoid wear and tear on its tires, and (b) finding the maximum permissible speed to avoid slipping.

### Part (a): Optimum Speed to Avoid Wear and Tear

1. **Understanding Forces on the Banked Track**:
- The car is on a banked circular track, which means it experiences gravitational force (mg) downward, normal force (N) perpendicular to the surface, and frictional force if necessary.
- The angle of banking is given as θ = 15°.

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