(A) : A maximum possible speed of a car on banked curved road is greater than that on a flat curved road
(R) : On a banked curved road horizontal component of normal reaction by road along with friction provides necessary centripetal force

Options

A. Both (A) and (R) are true and (R) is the correct explanation of (A)
B. Both (A) and (R) are true and (R) is not the
C. (A) is true but ( R) is false
D. Both (A) and (R ) are false

Answer

To solve the question, we need to analyze both the assertion (A) and the reason (R) provided.

### Step-by-Step Solution:

1. **Understanding the Assertion (A)**:
- The assertion states that the maximum possible speed of a car on a banked curved road is greater than that on a flat curved road.
- This is based on the fact that a banked road allows for better handling of the forces acting on the car, particularly at higher speeds.

**Hint**: Consider how the forces act differently on a banked road compared to a flat road.

2. **Analyzing the Forces on a Flat Curved Road**:
- On a flat curved road, the centripetal force required to keep the car moving in a circle is provided solely by the frictional force.
- The centripetal force \( F_c \) can be expressed as:
\[ F_c = \frac{mv^2}{r} \]
where \( m \) is the mass of the car, \( v \) is its speed, and \( r \) is the radius of the curve.
- The maximum frictional force available is given by:
\[ F_{\text{friction}} = \mu N \]
where \( \mu \) is the coefficient of friction and \( N \) is the normal force (equal to \( mg \) on a flat surface).

**Hint**: Think about how the frictional force limits the speed on a flat surface.

3. **Analyzing the Forces on a Banked Curved Road**:
- On a banked road, the normal force \( N \) acts at an angle \( \theta \) to the vertical.
- The normal force can be resolved into two components:
- A vertical component \( N \cos \theta \) balancing the weight of the car \( mg \).
- A horizontal component \( N \sin \theta \) providing the necessary centripetal force.
- The equation for centripetal force on a banked road becomes:
\[ F_c = N \sin \theta + F_{\text{friction}} \]
- This means that both the horizontal component of the normal force and the frictional force contribute to the centripetal force.

**Hint**: Consider how the angle of the bank affects the distribution of forces.

4. **Comparing Forces**:
- Since on a banked road both the horizontal component of the normal force and friction can act together to provide centripetal force, the maximum speed achievable on a banked road is higher than that on a flat road.
- Therefore, the assertion is true.

**Hint**: Reflect on how the combined forces on a banked road can support higher speeds.

5. **Understanding the Reason (R)**:
- The reason states that on a banked curved road, the horizontal component of the normal reaction, along with friction, provides the necessary centripetal force.
- This is indeed correct, as explained in the previous steps.

**Hint**: Think about how the components of forces work together on a banked road.

6. **Conclusion**:
- Both the assertion (A) and the reason (R) are true.
- The reason provided is a correct explanation for the assertion.

### Final Answer:
Both the assertion (A) and the reason (R) are true, and the reason is the correct explanation of the assertion.