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, we need to determine two things: (a) the optimum speed of the race car to avoid wear and tear on its tires, and (b) the maximum permissible speed to avoid slipping.

### Given Data:
- Radius of the racetrack, \( r = 300 \, \text{m} \)
- Angle of banking, \( \theta = 15^\circ \)
- Coefficient of friction, \( \mu = 0.2 \)

### (a) Optimum Speed Calculation
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