A car is moving along the horizontal banked curved road . At banked curvve road, the normal reaction is

Options

A. equal to weight
B. greater than weight
C. less than weight
D. less than or equal to weight

Answer

To solve the problem regarding the normal reaction on a car moving along a horizontal banked curved road, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding Forces on the Car**:
- When a car is moving on a banked curve, there are two main forces acting on it: the gravitational force (weight) acting downward, which is \( Mg \), and the normal reaction force \( N \) from the surface of the road acting perpendicular to the surface.

2. **Analyzing the Banked Curve**:
- The road is banked at an angle \( \theta \). The normal force \( N \) can be resolved into two components:
- A vertical component \( N \cos \theta \) that balances the weight of the car (\( Mg \)).
- A horizontal component \( N \sin \theta \) that provides the necessary centripetal force for circular motion.

3. **Setting Up the Equations**:
- For vertical forces:
\[ N \cos \theta = Mg \]
- For horizontal forces (centripetal force):
\[ N \sin \theta = \frac{Mv^2}{r} \]
Here, \( v \) is the speed of the car and \( r \) is the radius of the curve.

4. **Finding the Relationship Between \( N \) and \( Mg \)**:
- From the vertical force equation, we can express \( N \):
\[ N = \frac{Mg}{\cos \theta} \]
- Since \( \cos \theta \) is always less than or equal to 1, it follows that:
\[ N > Mg \]
This indicates that the normal reaction force \( N \) is greater than the weight of the car.

5. **Conclusion**:
- Therefore, the normal reaction on the car moving along a horizontal banked curved road is **greater than the weight** of the car.

### Final Answer:
The normal reaction is **greater than the weight** of the car.