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Q.

A railway track is banked for a speed v, by making the height of the outer rail h higher than that of the inner rail. The distance between the rails is d. The radius of curvature of the track is r 
 

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a

tansin-1hd=v2rg

b

tan-1hd=v2rg

c

hr=v2rg

d

hd=v2rg

answer is B.

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Detailed Solution

Ncosθ=mg and Nsinθ=mv2/r

So, tanθ=v2/rg

for train, AB= d and BB = h

sinθ=h/d⇒θ=sin-1( h/d)

tanθ=tansin-1( h/d)=v2/rg

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