Question

A railway track is banked by making the outer rail $10\text{cm}$ higher than the inner rail. The distance between the rails is $2\text{m}$. If the speed limit for trains on this track is $72\text{km/h}$, what will be the radius of curvature of the turn for safe travelling? Take $g=10{\text{m/s}}^2$.

• A. $80\text{m}$
• B. $500\text{m}$
• C. $800\text{m}$
  
• D. $1000\text{m}$

Answer 1

The correct option is C $800\text{m}$



From the figure of the track, we have
$\sin \theta =\frac{0.1}{2}=0.05$
Applying small angle approximation,
$\theta \approx \tan \theta \approx \sin \theta =0.05$

Also,$v=72\text{km/h}=72\times \frac{5}{18}=20\text{m/s}$


Applying the equation of circular dynamics:
$N\sin \theta =\frac{m{v}^2}{r}....\left(i\right)$
and $N\cos \theta =mg......\left(ii\right)$

Dividing $\left(i\right)$ by $\left(ii\right)$:
$\tan \theta =\frac{v^2}{rg}\Rightarrow 0.05=\frac{{20}^2}{r\times 10}\therefore r=800\text{m}$