The maximum safe speed of a vehicle over a curved road of radius 150 m is `10 m//s`. If the width of road is 7.5 m, the height of the outer edge will be

Options

A. 0.25 m
B. 0.50 m
C. 0.30 m
D. 0.60 m

Explanation

To solve the problem, we need to find the height of the outer edge of a curved road given the maximum safe speed, radius of the curve, and width of the road.

### Step-by-Step Solution:

1. **Identify Given Values**:
- Maximum safe speed (V) = 10 m/s
- Radius of the curve (r) = 150 m
- Width of the road (l) = 7.5 m

2. **Use the Formula for Maximum Speed**:
The maximum speed on a curved road can be expressed as:
\[ V_{\text{max}} = \sqrt{\mu \cdot r \cdot g} \]
where \( \mu \) is the coefficient of friction, \( r \) is the radius of the curve, and \( g \) is the acceleration due to gravity (approximately 10 m/s² for calculations).

3. **Relate Height to Speed and Road Width**:
The height of the outer edge (h) can be calculated using the formula:
\[ h = \frac{V^2 \cdot l}{r \cdot g} \]
where:
- \( V \) is the maximum speed,
- \( l \) is the width of the road,
- \( r \) is the radius of the curve,
- \( g \) is the acceleration due to gravity.

4. **Substitute the Known Values**:
Substitute the values into the formula:
\[ h = \frac{(10)^2 \cdot 7.5}{150 \cdot 10} \]

5. **Calculate the Numerator**:
\[ (10)^2 \cdot 7.5 = 100 \cdot 7.5 = 750 \]

6. **Calculate the Denominator**:
\[ 150 \cdot 10 = 1500 \]

7. **Calculate Height (h)**:
Now substitute the values into the equation:
\[ h = \frac{750}{1500} = 0.5 \text{ m} \]

8. **Conclusion**:
The height of the outer edge of the road is 0.5 meters.

### Final Answer:
The height of the outer edge will be **0.5 meters**.

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