Question

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

• A. 6 km / h
• B. 10 km / h
• C. 14 km / h
• D. 20 km / h

Answer 1

Answer: (A)

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