A train has to negotiate a curve of radius 400 m .The speed of the train is 72 km//h. If the distance between the two rails is 1 m ,then the outer rail will be raised over the inner rail by `(g=10m//s^(2))`

Options

A. 15 cm
B. 10 cm
C. 5 cm
D. 2.5 cm

Explanation

To solve the problem of how much the outer rail of a train should be raised over the inner rail while negotiating a curve, we can follow these steps:

### Step-by-Step Solution:

1. **Convert Speed from km/h to m/s**:
The speed of the train is given as 72 km/h. We need to convert this to meters per second (m/s) using the conversion factor \( \frac{5}{18} \).
\[ V = 72 \times \frac{5}{18} = 20 \, \text{m/s} \]

2. **Identify Given Values**:
- Radius of the curve, \( R = 400 \, \text{m} \)
- Acceleration due to gravity, \( g = 10 \, \text{m/s}^2 \)
- Distance between the rails, which we can consider as the horizontal distance, \( d = 1 \, \text{m} \)

3. **Use the Banking Angle Formula**:
The banking angle \( \theta \) can be derived from the formula:
\[ \tan \theta = \frac{V^2}{Rg} \]
Here, \( V \) is the speed, \( R \) is the radius, and \( g \) is the acceleration due to gravity.

4. **Substitute the Values**:
Substitute the known values into the formula:
\[ \tan \theta = \frac{(20)^2}{400 \times 10} \]
\[ \tan \theta = \frac{400}{4000} = \frac{1}{10} \]

5. **Relate the Height to the Distance Between Rails**:
Since the distance between the rails is 1 m, we can express the height \( H \) that the outer rail should be raised over the inner rail as:
\[ \tan \theta = \frac{H}{1} \]
Therefore, we have:
\[ H = \tan \theta \times 1 = \frac{1}{10} \times 1 = 0.1 \, \text{m} \]

6. **Final Result**:
The height \( H \) that the outer rail should be raised over the inner rail is:
\[ H = 0.1 \, \text{m} \, \text{or} \, 10 \, \text{cm} \]

### Conclusion:
The outer rail should be raised by **0.1 meters (10 centimeters)** to allow the train to negotiate the curve safely.