question_answer

A car is racing on a circular track of \[180\,\,m\] radius with a speed of \[32\,\,m{{s}^{-1}}\]. What should be the banking angle of the road to avoid chances of skidding of the vehicle at this speed without taking into consideration the friction between the tyre and the road?

A) \[{{45}^{o}}\]                                    

B) \[{{60}^{o}}\]

C) \[{{30}^{o}}\]                                    

D) \[{{15}^{o}}\]

Correct Answer: C

Solution :

To avoid dependence on friction, the rods are banked at the turn so that the outer part of the road is somewhat lifted compared to the inner part. Applying Newton's second law along the radius and the first law in the vertical direction.                 \[N\sin \theta =\frac{m{{v}^{2}}}{r}\] and        \[N\cos \theta =mg\] From these two equations, we get                 \[\tan \theta =\frac{{{v}^{2}}}{rg}\] Given,\[v=32\,\,m{{s}^{-1}},\,\,r=180\,\,m,\,\,g=9.8\,\,m/{{s}^{2}}\] Hence,  \[\tan \theta =\frac{{{(32)}^{2}}}{180\times 9.8}\] or                  \[\theta ={{30}^{o}}\]