A cyclist speeding at 4.5 km/h on a level road takes a sharp circular turn of radius 3 m without reducing the speed. The coefficient of static friction between the road and the tyres is 0.1.
(i) Will he slip while taking the turn?
(ii) Will he slip if his speed is 9 km/h?

Explanation

To solve the problem, we need to determine if the cyclist will slip while taking a sharp circular turn at two different speeds. We will use the concepts of centripetal force and friction.

### Given Data:
- Speed of cyclist (v1) = 4.5 km/h
- Speed of cyclist (v2) = 9 km/h
- Radius of turn (R) = 3 m
- Coefficient of static friction (μ) = 0.1
- Acceleration due to gravity (g) = 9.8 m/s²
...