(A): Two similar trains are moving along the equatorial line with the same speed but in opposite direction. They will exert equal pressure on the rails.
(R): In uniform circular motion the magnitude and direction of acceleration remains constant but the direction of motion continuously changes.

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 fals

Answer

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

### Step 1: Analyze the Assertion (A)
The assertion states that "Two similar trains are moving along the equatorial line with the same speed but in opposite directions. They will exert equal pressure on the rails."

- Both trains are similar and moving at the same speed but in opposite directions.
- Pressure exerted by an object is given by the formula:
\[ \text{Pressure} = \frac{\text{Force}}{\text{Area}} \]
- Since the trains are moving in opposite directions, they experience different forces due to the rotation of the Earth. One train moves with the direction of Earth's rotation, while the other moves against it.

### Step 2: Analyze the Forces Acting on the Trains
- The train moving with the Earth's rotation experiences a centripetal force \( F_{C2} \).
- The train moving against the Earth's rotation experiences a greater centripetal force \( F_{C1} \).
- Since the forces acting on each train are not equal, the pressures they exert on the rails will also not be equal.

### Conclusion for Assertion (A)
Thus, the assertion (A) is **false** because the two trains do not exert equal pressure on the rails.

### Step 3: Analyze the Reason (R)
The reason states that "In uniform circular motion, the magnitude and direction of acceleration remains constant, but the direction of motion continuously changes."

- In uniform circular motion, the magnitude of the centripetal acceleration remains constant, but the direction of the acceleration changes continuously as the object moves along the circular path.
- Therefore, the statement in the reason is incorrect because it claims that both the magnitude and direction of acceleration remain constant, which is not true.

### Conclusion for Reason (R)
Thus, the reason (R) is also **false** because only the magnitude of acceleration remains constant, while its direction changes.

### Final Conclusion
Both the assertion (A) and the reason (R) are false. Therefore, the correct answer is that both A and R are false.

### Summary of the Solution
- Assertion (A) is false because the two trains do not exert equal pressure on the rails due to different centripetal forces.
- Reason (R) is false because in uniform circular motion, only the magnitude of acceleration remains constant, while its direction changes.