Question

A cyclist speeding at $18km/h$ 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 0.1 . Will the cyclist slip while taking the turn?

• A. Yes, because $v\ge \sqrt{{\mu }_{s}gR}$
• B. Yes, because $v\le \sqrt{{\mu }_{s}gR}$
• C. No, because $v\le \sqrt{{\mu }_{s}gR}$
• D. None of these

Answer 1

Answer: (A)

Here, $v=18km/h,R=3m,{\mu }_s=0.1$
$\therefore \sqrt{{\mu }_{s}gR}=\sqrt{0.1\times 9.8\times 3}$
$=\sqrt{2.94}=1.71$
Also, $v=18km/h=\frac{18\times 1000}{60\times 60}$
$=5m/s$
Here, $v\ge \sqrt{{\mu }_{s}gR}$
So, cyclist will slip while taking the turn.