Question

A circular race track of radius $85\text{m}$ is banked at angle of ${37}^{\circ }$ If the coefficient of friction between the wheels of a race-car and the road is $0.2$, then the maximum possible speed to avoid slipping is $(\tan {37}^{\circ }=\frac{3}{4})$

• A. $\sqrt{950}\frac{m}{s}$
• B. $\sqrt{550}\frac{m}{s}$
• C. $\sqrt{1050}\frac{m}{s}$
• D. $\sqrt{850}\frac{m}{s}$

Answer 1

The correct option is A $\sqrt{950}\frac{m}{s}$

Given, radius of track $\left(r\right)=85m$
Banking angle $\left(\theta \right)={37}^{\circ }$
Coefficient of friction $\left(\mu \right)=0.2$
Maximum possible speed to avoid slipping is $v=\sqrt{\frac{rg(\mu +tan\theta )}{1-\mu tan\theta }}$
$=\sqrt{\frac{85\times 10(0.2+0.75)}{1-0.2\times 0.75}}$
$=\sqrt{\frac{850\left(0.95\right)}{0.85}}$

$=\sqrt{\frac{850\left(95\right)}{85}}=\sqrt{950}\frac{m}{s}$