(A) : A cyclist always bends inwards while negotiating a horizontal curve.
(r) : By bending, cyclist lowers his centre of gravity.

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 statements provided:

**Assertion (A):** A cyclist always bends inwards while negotiating a horizontal curve.
**Reason (R):** By bending, the cyclist lowers his center of gravity.

### Step-by-step Solution:

1. **Understanding the Assertion (A):**
- When a cyclist negotiates a horizontal curve, they lean inwards. This action helps them maintain balance and control while turning. The inward lean allows the cyclist to counteract the centrifugal force that acts outward when turning.

2. **Understanding the Reason (R):**
- The reason given states that by bending, the cyclist lowers his center of gravity. Lowering the center of gravity can indeed help in maintaining stability. However, the primary reason for bending inwards is to balance the forces acting on the cyclist during the turn.

3. **Evaluating the Truth of Each Statement:**
- Both statements are true:
- The assertion (A) is true because cyclists do bend inwards while turning.
- The reason (R) is also true because bending can lower the center of gravity, which aids in stability.

4. **Determining the Relationship between A and R:**
- While both statements are true, the reason (R) does not fully explain the assertion (A). The main reason for bending is to counteract the centrifugal force during the turn, not solely to lower the center of gravity.

5. **Conclusion:**
- Since both A and R are true, but R is not the correct explanation of A, the correct option is: "Both A and R are true and R is not the correct explanation of A."

### Final Answer:
Both A and R are true and R is not the correct explanation of A.