Question

A circular track of radius $300$ m is banked at an angle $\frac{\pi }{12}$ radian. If the coefficient of friction between wheel of a vehicle and road is $0.2$, the maximum safe speed of vehicle is :

• A. 28 $m{s}^{-1}$
• B. 38 $m{s}^{-1}$
• C. 18 $m{s}^{-1}$
• D. 48 $m{s}^{-1}$

Answer 1

The correct option is B 38 $m{s}^{-1}$

Maximum velocity,

$v_{max}={\left[\left(\frac{\mu +\tan \theta }{1-\mu \tan \theta }\right)rg\right]}^{1/2}$

$={[\left(\frac{0.2+\tan {15}^{\circ }}{1-0.2\tan {15}^{\circ }}\right)300\times 9.8]}^{1/2}$

$\simeq 38m{s}^{-1}$