question_answer

A vehicle is moving with a velocity u on a curved road of width b and radius of curvature R. For counteracting the centrifugal force on the vehicle, the difference in elevation required in between the outer and inner edges of the road is

A)  \[\frac{{{v}^{2}}b}{Rg}\]                               

B)         \[\frac{vb}{Rg}\]

C)  \[\frac{v{{b}^{2}}}{Rg}\]                             

D)         \[\frac{vb}{{{R}^{2}}g}\]

Correct Answer: A

Solution :

 Let \[\theta \] be the angle of banking to counteract the centrifugal force. Then             \[\tan \theta =\frac{{{v}^{2}}}{rg}\] If \[x\] is the elevation required, then             \[\sin \theta =\frac{x}{b}\] \[\Rightarrow \]   \[\theta =\sin \theta \approx \tan \theta =\frac{x}{b}\] \[\therefore \]      \[\frac{x}{b}=\frac{{{v}^{2}}}{Rg}\] \[\Rightarrow \]   \[x=\frac{{{v}^{2}}b}{Rg}\]