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Question

At certain place on railway track, the radius of curvature of railway track is 200 m. If the distance between the rails is 1.6 m, and the outer rail is raised by 0.08 m above the inner rail, find the speed of train for which there is no side pressure of the rails.
(Take g=10 m/s2)

A
5 m/s
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B
10 m/s
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C
15 m/s
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D
20 m/s
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Solution

The correct option is B 10 m/s

For equilibrium in vertical direction,
Ncosθ=mg...........(1)

Dynamics equation towards centre of circular curve,
Nsinθ=mv2rtanθ=v2rg.........(2)
Also,
Distance between rails is AB= 1.6 m and height between inner and outer rails, h= 0.08 m
sinθ=hL=0.081.6=120

As θ is small; sinθtanθ
Now putting value of tanθ in equation (2):
120=v2rgv=200×1020=10 m/s

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