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# A train rounds an unbanked circular bend of radius 50 m at a speed of $54\;km\;h^{-1}$. If $g= 10 \;m/s^{-2}$, the angle of banking required to prevent wearing out of rails is given by

$\begin{array}{1 1} \theta= \tan^{-1}(0.15) \\ \theta=\tan^{-1}(0.25) \\ \theta= \tan^{-1} (0.35) \\ \theta= \tan^{-1}(0.45) \end{array}$

Now $v= 54\;km\;h^{-1}=15 ms^{-1}$
$R= 50\;m$
The required angle of banking is given by
$\tan \theta = \large\frac{v^2}{Rg}$
$\qquad= \large\frac{15 \times 15}{50 \times 10}$
$\qquad= 0.45$