(A): A cyclist leans inwards while taking a turn, while a man sitting in a car leans outwards on a curve.
(R) : Centripetal acceleration is acting towards the centre of the curve.

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 correct explanation of (A)
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 1: Analyze the Assertion (A)
The assertion states: "A cyclist leans inwards while taking a turn, while a man sitting in a car leans outwards on a curve."

- When a cyclist takes a turn, they lean inwards to maintain balance and counteract the centrifugal force that acts outward. This leaning helps them stay upright and navigate the turn effectively.
- In contrast, a man sitting in a car leans outwards because the car's center of gravity does not coincide with the passenger's center of gravity. The outward lean is a reaction to the centrifugal force experienced during the turn.

**Conclusion for Step 1:** The assertion is true.

### Step 2: Analyze the Reason (R)
The reason states: "Centripetal acceleration is acting towards the centre of the curve."

- Centripetal acceleration is indeed directed towards the center of the curve for any object moving in a circular path. This acceleration is necessary for changing the direction of the object and keeping it in circular motion.
- In both cases (the cyclist and the car), centripetal acceleration acts towards the center of the curve, providing the necessary force to maintain the circular motion.

**Conclusion for Step 2:** The reason is also true.

### Step 3: Determine the Relationship Between A and R
Now, we need to check if the reason (R) correctly explains the assertion (A).

- The assertion describes the behavior of a cyclist and a passenger in a car during a turn, while the reason explains the underlying physics (centripetal acceleration) that allows both to navigate the turn.
- The leaning of the cyclist inwards and the passenger's leaning outwards can be understood through the concept of centripetal acceleration, as it explains the forces at play during the turn.

**Final Conclusion:** Both the assertion and the reason are true, and the reason is the correct explanation of the assertion.

### Answer:
**Option 1:** Both A and R are true, and R is the correct explanation of A.

---