Q] A railway track goes around a curve having a radius of curvature of

1.	Q] A railway track goes around a curve having a radius of curvature of 1 km. Thedistance between the rails is 1 m. Find the elevation of the outer rail above the inner rail so that there is no side pressure against the rails when a train goes round the curve at 36 km / hr.
Answer» Given, radius of CURVATURE, $\sf{r=1\ km=1000\ m}$ distance between the RAILS, $\sf{d=1\ m.}$ speed of the train, $\sf{v=36\ km\,h^{-1}=10\ m\,s^{-1}}$ Let $\sf{g=10\ m\,s^{-2}.}$ There WOULD be no side pressure against the rails when the train moves along the rail with MAXIMUM safe speed, which is given by, $\sf{\longrightarrow v^2=rg\tan\theta}$ Then the angle of ELEVATION will be, $\sf{\longrightarrow \theta=\tan^{-1}\left(\dfrac{v^2}{rg}\right)}$ $\sf{\longrightarrow \theta=\tan^{-1}\left(\dfrac{10^2}{1000\times10}\right)}$ $\sf{\longrightarrow \theta=\tan^{-1}\left(\dfrac{1}{100}\right)}$ $\sf{\longrightarrow \theta=0.01\ rad}$ Then the elevation of outer rail will be given by, $\sf{\longrightarrow h=d\sin\theta}$ $\sf{\longrightarrow h=1\times\sin(0.01)}$ $\sf{\longrightarrow\underline{\underline{h=0.01\ m}}}$