Laws of motion NCERT Solutions Class 11 Physics - Solved Exercise Question 5.31

Question 5.31:

A train runs along an unbanked circular track of radius 30 m at a speed of 54 km/h. The mass of the train is 10⁶ kg. What provides the centripetal force required for this purpose – The engine or the rails? What is the angle of banking required to prevent wearing out of the rail?

Solution:
Radius of the circular track, r = 30 m

Speed of the train, v = 54 km/h = 15 m/s
Mass of the train, m = 10⁶ kg
The centripetal force is provided by the lateral thrust of the rail on the wheel. As per Newton’s third law of motion, the wheel exerts an equal and opposite force on the rail. This reaction force is responsible for the wear and rear of the rail
The angle of banking θ, is related to the radius (r) and speed (v) by the relation:
tan θ = v² / rg
= 15² / (30 X 10)
= 225 / 300
θ = tan^-1 (0.75) = 36.87⁰
Therefore, the angle of banking is about 36.87°