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 `405"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 different speeds, we need to calculate the maximum speed (Vmax) at which the cyclist can turn without slipping, using the formula:

\[ V_{max} = \sqrt{\mu \cdot R \cdot g} \]

Where:
- \( \mu \) = coefficient of static friction = 0.1
- \( R \) = radius of the turn = 3 m
- \( g \) = acceleration due to gravity ≈ 10 m/s²
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