Question

A car has to move on a level turn of radius $45\text{m}$. If the coefficient of static friction between the tyres and the road is ${\mu }_s=0.5$, find the maximum speed the car can achieve without skidding.

• A. $54\text{km/h}$
• B. $18\text{km/h}$
• C. $30\text{km/h}$
• D. $40\text{km/h}$

Answer 1

The correct option is A $54\text{km/h}$

The limiting condition for velocity at a level turn is given by
$v\le \sqrt{{\mu }_{s}rg}$
For maximum velocity,
$v_{\text{max}}=\sqrt{{\mu }_{s}rg}$
$\Rightarrow v_{\text{max}}=\sqrt{0.5\times 10\times 45}$
$\Rightarrow v_{\text{max}}=15\text{m/s}$
$=15\times \frac{18}{5}=54\text{km/h}$