# A train has to negotiate a curve of radius $200\;m$ . By how much should the outer rails be raised with respect to the inner rails for a speed of $36\;km\;h^{-1}$. The distance between the rails is $1.5\;m$ Take $g=10 \;m /s^2$

$\begin{array}{1 1} 7.5\; cm \\ 10\;cm \\ 12.5\;cm \\ 15 \;cm \end{array}$

Speed of train $(v) =36\;km\;h^{-1}=10\;ms^{-1}$
Radius of the curve $(R) =200\;m$
Distance between rails $(x)=1.5 \;m$
Let the outer rails be raised by a height h with respect to the inner rails so that the angle of banking is $\theta$
Then $\tan \theta= \large\frac{h}{x}=\frac{v^2}{Rg}$
or $h= \large\frac{xv^2}{Rv}$
or $\qquad= 0.075\;m$
$\qquad= 7.5\;cm$
Answer: $7.5\; cm$