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 some what 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 \[\theta ={{30}^{o}}\]