Question

A circular race-car track of radius $300\text{m}$ is banked at an angle of ${15}^{\circ }$. If the coefficient of static friction between the wheels of the race-car and the road is $0.2$, what is the maximum permissible speed to avoid slipping? Take $\tan {15}^{\circ }=0.27,g=10{\text{m/s}}^2$.

• A. $48\text{m/s}$
• B. $30\text{m/s}$
• C. $17\text{m/s}$
• D. $38.60\text{m/s}$

Answer 1

The correct option is D $38.60\text{m/s}$

Here, $r=300\text{m},\theta ={15}^{\circ },g=10{\text{m/s}}^2$ and ${\mu }_s=0.2$
The maximum permissible speed to avoid slipping $v_{\text{max}}$ is given by:
$v_{\text{max}}=\sqrt{\left(\frac{rg({\mu }_s+\tan \theta )}{1-{\mu }_s\tan \theta }\right)}$
$v_{\text{max}}=\sqrt{\left(\frac{300\times 10\times (0.2+0.27)}{1-\left(0.2\right)\left(0.27\right)}\right)}$
$v_{\text{max}}=38.60\text{m/s}$