Question

A circular racket of radius 300 m is backed at an angle of ${15}^0$. The coefficient of friction between the wheels of a race car and the road is 0.2. the maximum permissible speed to avoid slipping is
( Take tan ${15}^0=0.27,g=10m{s}^{-2}$)

• A. 18.6 $m{s}^{-1}$
• B. 28.6 $m{s}^{-1}$
• C. 38.6 $m{s}^{-1}$
• D. 48.6 $m{s}^{-1}$

Answer 1

Answer: (C)

38.6 $m{s}^{-1}$

$\begin{array}{c}r=300m\\ \theta ={15}^o\\ \mu =0.2\end{array}$
$\begin{array}{c}\tan {15}^o=\tan \left(45-30\right)=\frac{\tan 45-\tan 30}{1+\tan 45\tan 30}\\ =\frac{1-\frac{1}{\sqrt{3}}}{1+1\times \frac{1}{\sqrt{3}}}=\frac{0.422}{1.57}=0.26\end{array}$
The maximum permissible speed is given by
$\begin{array}{c}{V}_{max}=\sqrt{\frac{rg(\mu +tan\theta )}{1-\mu tan\theta }}=\sqrt{\frac{300\times 10\times (0.2+0.27)}{1-0.2\times 0.27}}\\ =38.6m{s}^{-1}\end{array}$