Assertion: When water in a bucket is whirled fast overhead, the water does not fall out at the top of the ciorcular path.
Reason: The centripetal force in this position on water is more than the weight of water.

Options

A. If both Assertion and Reason are true and the Reason is correct explanation of the Assertion.
B. If both Assertion and Reason are true but Reason is not the correct explanation of Assertion.
C. If Assertion is true, true but the Reason is false.
D. If Assertion is false but the Reason is true.

Explanation

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

### Step-by-Step Solution:

1. **Understanding the Assertion**:
- The assertion states that when a bucket filled with water is whirled overhead in a circular motion, the water does not fall out at the top of the circular path.
- This phenomenon can be observed when the bucket is rotated with sufficient speed.

2. **Understanding the Reason**:
- The reason given is that the centripetal force acting on the water at the top of the circular path is greater than the weight of the water.
- Centripetal force is the force required to keep an object moving in a circular path and is directed towards the center of the circle.

3. **Analyzing Forces at the Top of the Circular Path**:
- At the top of the circular path, two forces act on the water:
- The gravitational force (weight of the water) acting downwards.
- The centripetal force required to keep the water moving in a circular path, which is also directed downwards at this point.
- For the water to remain in the bucket and not fall out, the centripetal force must be equal to or greater than the gravitational force.

4. **Condition for Water to Stay in the Bucket**:
- If the centripetal force is greater than the gravitational force, the water will stay in the bucket.
- The centripetal force can be expressed as \( F_c = \frac{mv^2}{r} \), where \( m \) is the mass of the water, \( v \) is the velocity of the bucket, and \( r \) is the radius of the circular path.
- The gravitational force can be expressed as \( F_g = mg \), where \( g \) is the acceleration due to gravity.

5. **Conclusion**:
- When the bucket is whirled fast enough, the centripetal force indeed becomes greater than the weight of the water, allowing the water to stay in the bucket without falling out.
- Therefore, both the assertion and the reason are true, and the reason correctly explains the assertion.

### Final Answer:
Both the assertion and the reason are true, and the reason is a correct explanation of the assertion.

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