Question

Which one of the following statements is TRUE?

• A. Cant deficiency is related to train moving faster, and Cant excess is related to train moving slower.
• B. Cant deficiency is related to train moving slower, and Cant excess is related to train moving faster.
• C. Cant deficiency is related to train moving on the main line, and Cant excess is related to train moving on the branch line.
• D. Cant deficiency is related to train moving on the branch line, and Cant excess is related to train moving on the main line.

Hint:

Compare actual cant provided to the equilibrium cant needed at the train's actual speed: too little cant for a fast train is deficiency, too much cant for a slow train is excess.

Answer 1

The Correct Option is A

Step 1: Understanding the Question:
On a curved railway track, cant (superelevation) is the difference in height between the outer and inner rail, provided to balance the centrifugal force acting on a train as it goes around the curve. The cant that exactly balances the centrifugal force at a chosen speed is called the equilibrium cant.

Step 2: Key Formula or Approach:
Actual cant provided on the track is fixed for a curve, but trains pass over that curve at different speeds. Comparing the actual cant to the equilibrium cant needed at the actual running speed gives two possible situations:
\[ \text{Cant deficiency} = \text{Equilibrium cant at running speed} - \text{Actual cant provided} \]
\[ \text{Cant excess} = \text{Actual cant provided} - \text{Equilibrium cant at running speed} \]

Step 3: Detailed Explanation:
If a train runs faster than the speed for which the actual cant was designed, it needs more cant than what is provided to fully balance the centrifugal force, so the track is short of the cant that speed demands. This shortfall is cant deficiency, and it is linked to a train moving faster than the equilibrium speed.
If a train runs slower than the design speed, the actual cant provided is more than what that lower speed needs to stay balanced, so there is extra cant beyond requirement. This surplus is cant excess, and it is linked to a train moving slower than the equilibrium speed.
Options (C) and (D) describe cant deficiency and excess in terms of main line versus branch line running, but that is a separate, secondary application seen at turnouts where main line and branch line speeds differ; the fundamental definition of cant deficiency and cant excess is tied to speed relative to equilibrium speed, not to which line the train is on. So (C) and (D) do not state the basic, general TRUE definition.

Step 4: Final Answer:
Cant deficiency occurs when the train moves faster than the equilibrium speed, and cant excess occurs when the train moves slower than the equilibrium speed. This matches option (A).