Question

A curved section of a road is banked for a speed v. If there is no friction between the road and the tyres then 

(a) a car moving with speed v will not slip on the road 

(b) a car is more likely to slip on the road at speeds higher than v, than at speeds lower than v 

(c) a car is more likely to slip on the road at speeds lower than v, than at speeds higher than v 

(d) a car can remain stationary on the road without slipping

Answer 1

Correct Answer is: (a) a car moving with speed v will not slip on the road

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.