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A hollow sphere is filled with water. It is hung by a long thread. As the water flows out of a hole at the bottom, the period of oscillation will [1997]
- a)first increase and then decrease
- b)first decrease and then increase
- c)go on increasing
- d)go on decreasing
Correct answer is option 'A'. Can you explain this answer?
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Verified Answer
A hollow sphere is filled with water. It is hung by a long thread. As ...
Time period of simple pendulum
where l is effectivelength. [i.e distance between centre of suspension and centre of gravity of bob]
Initially, centre of gravity is at the centre of sphere. When water leaks the centre of gravity goes down until it is half filled; then it begins to go up and finally it again goes at the centre. That is effective length first increases and then decreases. As 
, so time period first increases and then decreases.
, so time period first increases and then decreases.Most Upvoted Answer
A hollow sphere is filled with water. It is hung by a long thread. As ...
The period of oscillation of a hollow sphere filled with water and hung by a long thread will first increase and then decrease as the water flows out of a hole at the bottom.
Explanation:
When the hollow sphere is filled with water, it gains mass and therefore its moment of inertia increases. The moment of inertia is a measure of an object's resistance to changes in its rotational motion.
Initial Period of Oscillation:
Initially, when the sphere is filled with water, the period of oscillation is determined by the moment of inertia of the sphere filled with water. Let's denote this period as T1.
As Water Flows Out:
As the water flows out of the sphere through the hole at the bottom, the mass of the sphere decreases. This leads to a decrease in the moment of inertia of the sphere.
Decrease in Moment of Inertia:
As the moment of inertia decreases, the period of oscillation of the sphere also decreases. Let's denote this period as T2.
Minimum Moment of Inertia:
At a certain point, all the water has flowed out of the sphere, and the moment of inertia reaches its minimum value.
Maximum Period of Oscillation:
At this point, the period of oscillation reaches its minimum value T2.
Increasing Moment of Inertia:
After all the water has flowed out, if the sphere continues to oscillate, the period of oscillation starts to increase again. This is because as the sphere rotates, the water starts to accumulate on one side due to the centrifugal force. This accumulation of water increases the moment of inertia of the sphere, leading to an increase in the period of oscillation.
Maximum Moment of Inertia:
The moment of inertia reaches its maximum value when all the water has accumulated on one side of the sphere.
Decreasing Period of Oscillation:
As the moment of inertia decreases again, the period of oscillation starts to decrease. This continues until the water flows out of the hole, and the sphere becomes empty.
Therefore, the period of oscillation of the hollow sphere filled with water first increases and then decreases as the water flows out of the hole at the bottom.
Explanation:
When the hollow sphere is filled with water, it gains mass and therefore its moment of inertia increases. The moment of inertia is a measure of an object's resistance to changes in its rotational motion.
Initial Period of Oscillation:
Initially, when the sphere is filled with water, the period of oscillation is determined by the moment of inertia of the sphere filled with water. Let's denote this period as T1.
As Water Flows Out:
As the water flows out of the sphere through the hole at the bottom, the mass of the sphere decreases. This leads to a decrease in the moment of inertia of the sphere.
Decrease in Moment of Inertia:
As the moment of inertia decreases, the period of oscillation of the sphere also decreases. Let's denote this period as T2.
Minimum Moment of Inertia:
At a certain point, all the water has flowed out of the sphere, and the moment of inertia reaches its minimum value.
Maximum Period of Oscillation:
At this point, the period of oscillation reaches its minimum value T2.
Increasing Moment of Inertia:
After all the water has flowed out, if the sphere continues to oscillate, the period of oscillation starts to increase again. This is because as the sphere rotates, the water starts to accumulate on one side due to the centrifugal force. This accumulation of water increases the moment of inertia of the sphere, leading to an increase in the period of oscillation.
Maximum Moment of Inertia:
The moment of inertia reaches its maximum value when all the water has accumulated on one side of the sphere.
Decreasing Period of Oscillation:
As the moment of inertia decreases again, the period of oscillation starts to decrease. This continues until the water flows out of the hole, and the sphere becomes empty.
Therefore, the period of oscillation of the hollow sphere filled with water first increases and then decreases as the water flows out of the hole at the bottom.
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A hollow sphere is filled with water. It is hung by a long thread. As the water flows out of a hole at the bottom, the period of oscillation will [1997]a)first increase and then decreaseb)first decrease and then increasec)go on increasingd)go on decreasingCorrect answer is option 'A'. Can you explain this answer?
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A hollow sphere is filled with water. It is hung by a long thread. As the water flows out of a hole at the bottom, the period of oscillation will [1997]a)first increase and then decreaseb)first decrease and then increasec)go on increasingd)go on decreasingCorrect answer is option 'A'. Can you explain this answer? for NEET 2024 is part of NEET preparation. The Question and answers have been prepared according to the NEET exam syllabus. Information about A hollow sphere is filled with water. It is hung by a long thread. As the water flows out of a hole at the bottom, the period of oscillation will [1997]a)first increase and then decreaseb)first decrease and then increasec)go on increasingd)go on decreasingCorrect answer is option 'A'. Can you explain this answer? covers all topics & solutions for NEET 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A hollow sphere is filled with water. It is hung by a long thread. As the water flows out of a hole at the bottom, the period of oscillation will [1997]a)first increase and then decreaseb)first decrease and then increasec)go on increasingd)go on decreasingCorrect answer is option 'A'. Can you explain this answer?.
A hollow sphere is filled with water. It is hung by a long thread. As the water flows out of a hole at the bottom, the period of oscillation will [1997]a)first increase and then decreaseb)first decrease and then increasec)go on increasingd)go on decreasingCorrect answer is option 'A'. Can you explain this answer? for NEET 2024 is part of NEET preparation. The Question and answers have been prepared according to the NEET exam syllabus. Information about A hollow sphere is filled with water. It is hung by a long thread. As the water flows out of a hole at the bottom, the period of oscillation will [1997]a)first increase and then decreaseb)first decrease and then increasec)go on increasingd)go on decreasingCorrect answer is option 'A'. Can you explain this answer? covers all topics & solutions for NEET 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A hollow sphere is filled with water. It is hung by a long thread. As the water flows out of a hole at the bottom, the period of oscillation will [1997]a)first increase and then decreaseb)first decrease and then increasec)go on increasingd)go on decreasingCorrect answer is option 'A'. Can you explain this answer?.
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A hollow sphere is filled with water. It is hung by a long thread. As the water flows out of a hole at the bottom, the period of oscillation will [1997]a)first increase and then decreaseb)first decrease and then increasec)go on increasingd)go on decreasingCorrect answer is option 'A'. Can you explain this answer?, a detailed solution for A hollow sphere is filled with water. It is hung by a long thread. As the water flows out of a hole at the bottom, the period of oscillation will [1997]a)first increase and then decreaseb)first decrease and then increasec)go on increasingd)go on decreasingCorrect answer is option 'A'. Can you explain this answer? has been provided alongside types of A hollow sphere is filled with water. It is hung by a long thread. As the water flows out of a hole at the bottom, the period of oscillation will [1997]a)first increase and then decreaseb)first decrease and then increasec)go on increasingd)go on decreasingCorrect answer is option 'A'. Can you explain this answer? theory, EduRev gives you an
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