A cyclist speeding at `4.5"km h"^(-1)` 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` will the cyclist slip while taking the turn (i) with a speed of `4.5"km h"^(-1)` and (ii) with a speed of `9 "km k^(-1)`?

Explanation

To determine whether the cyclist will slip while taking a turn at two different speeds, we can follow these steps:

### Step 1: Understand the Forces Acting on the Cyclist
When a cyclist takes a turn, the necessary centripetal force to keep the cyclist moving in a circular path is provided by the static friction between the tires and the road. The forces acting on the cyclist are:
- The gravitational force (weight) acting downwards: \( mg \)
- The normal force acting upwards: \( N \)
- The static friction force providing the centripetal force: \( f_s \)

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