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 whether the cyclist will slip while taking a turn at two different speeds: 4.5 km/h and 9 km/h.

### Given Data:
- Speed of the cyclist, \( v_1 = 4.5 \, \text{km/h} \)
- Speed of the cyclist, \( v_2 = 9 \, \text{km/h} \)
- Radius of the turn, \( r = 3 \, \text{m} \)
- Coefficient of static friction, \( \mu = 0.1 \)

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