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  4. A cyclist speeding at v 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 tyres and the road is 0.1 . The maximum speed of the cyclist for him not to slip is about

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Q. A cyclist speeding at $v km / h$ on a level road takes a sharp circular turn of radius $3 m$ without reducing the speed. The coefficient of static friction between the tyres and the road is $0.1 .$ The maximum speed of the cyclist for him not to slip is about

System of Particles and Rotational Motion

Solution:

The condition for the cyclist not to slip is given by
$v<\sqrt{\mu_{ s } \cdot R \cdot g}$
$ \Rightarrow v <\, \sqrt{(0.1)(3 m )\left(9.8 m / s ^{2}\right)}$
$v<\, 1.71 m / s$
$ \Rightarrow v <\, \left(1.71 \times \frac{18}{5}\right) km / h \approx 6\, km / h$