The angle of banking for a railway track is given by ` theta =sin ^(-1) ((1)/(16))` . If it is a metre gauge railway line , then the elevation of the outer rail above the inner rail is

Options

A. `5cm`
B. `625 cm`
C. `10 cm `
D. `12.5 cm`

Explanation

To solve the problem of finding the elevation of the outer rail above the inner rail for a meter gauge railway line given the angle of banking, we can follow these steps:

### Step-by-Step Solution

1. **Identify the Given Information:**
- The angle of banking, \( \theta = \sin^{-1}\left(\frac{1}{16}\right) \)
- Length of the railway line (gauge), \( L = 1 \) meter

2. **Calculate \( \sin \theta \):**
- From the given angle, we have:
\[ \sin \theta = \frac{1}{16} \]

3. **Use the Relationship Between Height and Length:**
- The elevation \( H \) of the outer rail above the inner rail can be calculated using the formula:
\[ H = L \cdot \sin \theta \]

4. **Substitute the Values:**
- Substitute \( L = 1 \) meter and \( \sin \theta = \frac{1}{16} \):
\[ H = 1 \cdot \frac{1}{16} = \frac{1}{16} \text{ meters} \]

5. **Convert the Height to Centimeters:**
- Since \( 1 \text{ meter} = 100 \text{ centimeters} \):
\[ H = \frac{1}{16} \times 100 = 6.25 \text{ centimeters} \]

6. **Final Result:**
- The elevation of the outer rail above the inner rail is:
\[ H = 6.25 \text{ cm} \]

### Final Answer:
The elevation of the outer rail above the inner rail is **6.25 cm**.

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