Question

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

• A. Yes, because $v \geq \sqrt{\mu_{s} g R}$
• B. Yes, because $v \leq \sqrt{\mu_{s} g R}$
• C. No, because $v \leq \sqrt{\mu_{s} g R}$
• D. None of these

Answer 1

Answer: (A)

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