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Question

A metre gauge train is moving at a speed of 36 km/hr along a curved track of radius 10√3 m. Find the height of the outer rail with respect to the inner rail, so that there is no side pressure on the rails. Take g=10 m/s2 and the width of the track to be 1 m.

A
0.8 m
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B
1 m
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C
0.6 m
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D
0.5 m
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Solution

The correct option is D 0.5 mFBD of the train on the curved track is shown below. Let the angle of banking be θ. To avoid side pressure on rails, dependency on frictional force for providing centripetal force should be eliminated, by opting for banking of track. For a metre gauge train, the distance between outer and inner rail is AB=1 m. The train is moving with speed v=36 km/hr×518=10 m/s, and r=10√3 m From the FBD, Nsinθ=mv2r....(i) Ncosθ=mg.....(ii) Dividing (i) by (ii), tanθ=v2rg=10210√3×10=1√3 ⇒θ=tan−1(1√3)=30∘ From triangle ABC in the figure, h= AB×sin30∘=1 m×12=0.5 m

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