Why are the curved roads banked ? Obtain an expression for angle of banking of a curved road .

Explanation

### Step-by-Step Solution

1. **Understanding the Problem**:
- Curved roads are banked to help vehicles navigate turns safely without slipping off the road. The banking angle allows the normal force to provide the necessary centripetal force for the vehicle to follow a curved path.

2. **Identify Forces Acting on the Vehicle**:
- When a vehicle of mass \( M \) moves with a velocity \( v_0 \) along a curved path of radius \( r \), it requires a centripetal force to maintain its circular motion. The centripetal force \( F_c \) is given by:
\[
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