The radius of curvature of railway line at a place is 200 m. If the distance between the rail is 1.6 m and the outer rail is raised by 0.08 m above the inner rail .The speed of the train for which there is no side pressure on the rails `(g=10 m//s^(2))`

Options

A. `5 m//s`
B. `10 m//s`
C. `15 m//s`
D. `20 m//s`

Explanation

To solve the problem, we need to find the speed of the train for which there is no side pressure on the rails. We will use the concept of banking of roads and the forces acting on the train.

### Step-by-Step Solution:

1. **Identify the Given Data:**
- Radius of curvature (R) = 200 m
- Distance between the rails (d) = 1.6 m
- Height of the outer rail above the inner rail (h) = 0.08 m
- Acceleration due to gravity (g) = 10 m/s²

2. **Calculate the Banking Angle (θ):**
The banking angle can be calculated using the formula:
\[ \tan(\theta) = \frac{h}{d} \]
Substituting the values:
\[ \tan(\theta) = \frac{0.08}{1.6} = 0.05 \]
Now, we can find θ using the arctan function:
\[ \theta = \tan^{-1}(0.05) \]

3. **Calculate the Speed of the Train (v):**
The formula for the speed of a train on a banked curve without side pressure is given by:
\[ v = \sqrt{R \cdot g \cdot \tan(\theta)} \]
We already have R and g, and we can use the value of \(\tan(\theta)\) we calculated earlier.
Substituting the values:
\[ v = \sqrt{200 \cdot 10 \cdot 0.05} \]
\[ v = \sqrt{200 \cdot 0.5} = \sqrt{100} = 10 \text{ m/s} \]

4. **Final Answer:**
The speed of the train for which there is no side pressure on the rails is **10 m/s**.