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The bob of a simple pendulum is a spherical hollow ball filled with water. A plugged hole near the bottom of the oscillating bob gets suddenly unplugged. During observation, till water is coming out, the time period of oscillation would
- a)first decrease and then increase to the original value
- b)first increase and then decrease to the original value
- c)increase towards a saturation value
- d)remain unchanged
Correct answer is option 'B'. Can you explain this answer?
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Verified Answer
The bob of a simple pendulum is a spherical hollow ball filled with wa...
Centre of mass of combination of liquid and hollow portion (at position ℓ), first goes down (to ℓ + Δℓ) and when total water is drained out, centre of mass regain its original position (to ℓ),
∴ ‘T’ first increases and then decreases to original value.
Most Upvoted Answer
The bob of a simple pendulum is a spherical hollow ball filled with wa...
Explanation:
When the hole near the bottom of the oscillating bob gets suddenly unplugged, water starts to flow out of the bob. This change in the distribution of mass affects the time period of oscillation of the pendulum.
Initial Situation:
- The bob of the pendulum is filled with water, creating a certain distribution of mass.
- The time period of oscillation of the pendulum in this initial situation is denoted as T.
When the hole is unplugged:
- As the hole near the bottom of the bob is unplugged, water starts to flow out of the bob.
- This results in a decrease in the mass of the bob as water leaves the bob.
- Due to the decrease in mass, the moment of inertia of the bob decreases.
- According to the formula for the time period of a simple pendulum, T = 2π√(L/g), where L is the length of the pendulum and g is the acceleration due to gravity.
- As the moment of inertia decreases, the time period of oscillation increases.
Water continues to flow out:
- As water continues to flow out of the bob, the mass of the bob keeps decreasing.
- This leads to a further decrease in the moment of inertia and an increase in the time period of oscillation.
When all the water has flowed out:
- After a certain period of time, all the water will have flowed out of the bob.
- At this point, the mass of the bob becomes constant and equal to the original mass of the hollow ball without water.
- The moment of inertia of the bob also becomes constant.
- As a result, the time period of oscillation of the pendulum reaches its maximum value.
After all the water has flowed out:
- Once all the water has flowed out, the mass and moment of inertia of the bob remain constant.
- Therefore, the time period of oscillation of the pendulum returns to its original value, denoted as T.
Conclusion:
- From the above explanation, it is clear that when the hole near the bottom of the oscillating bob gets suddenly unplugged, the time period of oscillation of the pendulum first increases and then decreases to the original value. Therefore, option 'B' is the correct answer.
When the hole near the bottom of the oscillating bob gets suddenly unplugged, water starts to flow out of the bob. This change in the distribution of mass affects the time period of oscillation of the pendulum.
Initial Situation:
- The bob of the pendulum is filled with water, creating a certain distribution of mass.
- The time period of oscillation of the pendulum in this initial situation is denoted as T.
When the hole is unplugged:
- As the hole near the bottom of the bob is unplugged, water starts to flow out of the bob.
- This results in a decrease in the mass of the bob as water leaves the bob.
- Due to the decrease in mass, the moment of inertia of the bob decreases.
- According to the formula for the time period of a simple pendulum, T = 2π√(L/g), where L is the length of the pendulum and g is the acceleration due to gravity.
- As the moment of inertia decreases, the time period of oscillation increases.
Water continues to flow out:
- As water continues to flow out of the bob, the mass of the bob keeps decreasing.
- This leads to a further decrease in the moment of inertia and an increase in the time period of oscillation.
When all the water has flowed out:
- After a certain period of time, all the water will have flowed out of the bob.
- At this point, the mass of the bob becomes constant and equal to the original mass of the hollow ball without water.
- The moment of inertia of the bob also becomes constant.
- As a result, the time period of oscillation of the pendulum reaches its maximum value.
After all the water has flowed out:
- Once all the water has flowed out, the mass and moment of inertia of the bob remain constant.
- Therefore, the time period of oscillation of the pendulum returns to its original value, denoted as T.
Conclusion:
- From the above explanation, it is clear that when the hole near the bottom of the oscillating bob gets suddenly unplugged, the time period of oscillation of the pendulum first increases and then decreases to the original value. Therefore, option 'B' is the correct answer.
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The bob of a simple pendulum is a spherical hollow ball filled with water. A plugged hole near the bottom of the oscillating bob gets suddenly unplugged. During observation, till water is coming out, the time period of oscillation woulda)first decrease and then increase to the original valueb)first increase and then decrease to the original valuec)increase towards a saturation valued)remain unchangedCorrect answer is option 'B'. Can you explain this answer?
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The bob of a simple pendulum is a spherical hollow ball filled with water. A plugged hole near the bottom of the oscillating bob gets suddenly unplugged. During observation, till water is coming out, the time period of oscillation woulda)first decrease and then increase to the original valueb)first increase and then decrease to the original valuec)increase towards a saturation valued)remain unchangedCorrect answer is option 'B'. Can you explain this answer? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about The bob of a simple pendulum is a spherical hollow ball filled with water. A plugged hole near the bottom of the oscillating bob gets suddenly unplugged. During observation, till water is coming out, the time period of oscillation woulda)first decrease and then increase to the original valueb)first increase and then decrease to the original valuec)increase towards a saturation valued)remain unchangedCorrect answer is option 'B'. Can you explain this answer? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The bob of a simple pendulum is a spherical hollow ball filled with water. A plugged hole near the bottom of the oscillating bob gets suddenly unplugged. During observation, till water is coming out, the time period of oscillation woulda)first decrease and then increase to the original valueb)first increase and then decrease to the original valuec)increase towards a saturation valued)remain unchangedCorrect answer is option 'B'. Can you explain this answer?.
The bob of a simple pendulum is a spherical hollow ball filled with water. A plugged hole near the bottom of the oscillating bob gets suddenly unplugged. During observation, till water is coming out, the time period of oscillation woulda)first decrease and then increase to the original valueb)first increase and then decrease to the original valuec)increase towards a saturation valued)remain unchangedCorrect answer is option 'B'. Can you explain this answer? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about The bob of a simple pendulum is a spherical hollow ball filled with water. A plugged hole near the bottom of the oscillating bob gets suddenly unplugged. During observation, till water is coming out, the time period of oscillation woulda)first decrease and then increase to the original valueb)first increase and then decrease to the original valuec)increase towards a saturation valued)remain unchangedCorrect answer is option 'B'. Can you explain this answer? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The bob of a simple pendulum is a spherical hollow ball filled with water. A plugged hole near the bottom of the oscillating bob gets suddenly unplugged. During observation, till water is coming out, the time period of oscillation woulda)first decrease and then increase to the original valueb)first increase and then decrease to the original valuec)increase towards a saturation valued)remain unchangedCorrect answer is option 'B'. Can you explain this answer?.
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