Question

A railway track is banked for a speed $v$, by making the height of the outer rail ' $h$ ' higher than that of the inner rail. The horizontal separation between the rails is $d$. The radius of curvature of the track is ' $r$ ' : then which of the following relation is true?

• A. $\frac{h}{d}=\frac{v^{2}}{r g}$
• B. $\tan \left(\sin ^{-1} \frac{h}{d}\right)=\frac{v^{2}}{r g}$
• C. $\tan ^{-1}\left(\frac{h}{d}\right)=\frac{v^{2}}{r g}$
• D. $\frac{h}{r}=\frac{v^{2}}{d g}$

Answer 1

Answer: (A)

$\tan \theta=\frac{v^{2}}{R g}$
and $\frac{h}{d}=\tan \theta$