Assertion:- Two identical trains move in opposte sense in equatorial plane with equal speed reltative to earth's surface. They have equal magnitude of normal reaction.
Reason:- The trains require same centripetal force although they have different speeds.

Options

A. If both Assertion `&` Reason are True `&` the Reason is a correct explanation of the Assertion.
B. If both Assertion `&` Reason are True but Reason is not a correct explanation of the Assertion.
C. If Assertion is True but the Reason is False.
D. If both Assertion `&` Reason are False.

Answer

To solve the given question, we need to analyze the assertion and the reason provided.

### Step 1: Understand the Assertion
The assertion states that two identical trains are moving in opposite directions in the equatorial plane with equal speed relative to the Earth's surface and that they have equal magnitudes of normal reaction.

### Step 2: Analyze the Reason
The reason provided states that the trains require the same centripetal force, although they have different speeds.

### Step 3: Evaluate the Assertion
- Since both trains are identical and moving with equal speed relative to the Earth's surface, they will experience the same gravitational force acting downwards and the same normal force acting upwards.
- Therefore, the magnitudes of the normal reactions acting on both trains will indeed be equal.

### Step 4: Evaluate the Reason
- The centripetal force required for circular motion is given by the formula \( F_c = \frac{mv^2}{r} \), where \( m \) is the mass of the train, \( v \) is the speed, and \( r \) is the radius of the circular path.
- In this case, since the trains are moving at equal speeds (as stated in the assertion), they will require the same centripetal force to maintain their circular motion.

### Step 5: Conclusion
- Both the assertion and the reason are true.
- However, the reason does not correctly explain the assertion. The assertion is true because of equal speeds and identical nature of the trains, while the reason incorrectly states that they require different centripetal forces.

### Final Answer
- Assertion: True
- Reason: True
- The reason does not correctly explain the assertion.

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