Question

At certain place on railway track, the radius of curvature of railway track is $200\text{m}$. If the distance between the rails is $1.6\text{m}$, and the outer rail is raised by $0.08\text{m}$ above the inner rail, find the speed of train for which there is no side pressure of the rails.
(Take $g=10{\text{m/s}}^2$)

• A. $5\text{m/s}$
• B. $15\text{m/s}$
• C. $20\text{m/s}$
• D. $10\text{m/s}$

Answer 1

The correct option is D $10\text{m/s}$


$\Rightarrow$ For equilibrium in vertical direction,
$N\cos \theta =mg$...........(1)

$\Rightarrow$ Dynamics equation towards centre of circular curve,
$N\sin \theta =\frac{m{v}^2}{r}\Rightarrow \tan \theta =\frac{v^2}{rg}$.........(2)
Also,
Distance between rails is $AB=1.6m$ and height between inner and outer rails, $h=0.08m$
$\therefore$$\sin \theta =\frac{h}{L}=\frac{0.08}{1.6}=\frac{1}{20}$

As ${}^{\prime }{\theta }^{\prime }$ is small; $\sin \theta \simeq \tan \theta$
Now putting value of $\tan \theta$ in equation (2):
$\Rightarrow \frac{1}{20}=\frac{v^2}{rg}\Rightarrow v=\sqrt{\frac{200\times 10}{20}}=10\text{m/s}$