Question

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.

(a) h/d = v²/rg

(b) tan (Sin ^-1 h/d) = v²/rg

(c) tan ^-1 (h/d) = v²/rg

(d) d/r = v²/dg

Answer 1

Correct Answer is:(b) tan (Sin ^-1 h/d) = v²/rg

The horizontal component of N supplies the necessary centripetal force.

Nsin θ = mv ²/r

Hence a car moving with a speed v does not slip even if there is no friction.

For any speed other than v, either higher or lower than v, the above condition is not satisfied, and the car will slip. This is true for v = 0 also, i.e., for a stationary car.

Also, Ncos θ = mg ∴ tan θ = v ²/rg

For the railway track, AB = d, BC = h, sin θ = h/d

or θ = Sin^-1(h/d)  or tan (Sin ^-1 h/d) = v²/rg.