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A horizontal wheel with light buckets fixed on its circumference revolves about a frictionless and vertical axis. Water falling from a fixed tap with a uniform rate of mass $m$ per unit of time is collected by the buckets. Denote $I$ and $r$ as the initial moment of inertia of the entire system about the axis and the radius of the wheel respectively. Is it necessary that the mass rate at which water falls on the buckets will be constant over time'?

As the question says its what happening so how can one do that?

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My reasoning is like as the angular velocity of water is changing with time so the rotation speed is changing so it would take less/more time compared to initially for water to fill $m$ mass isnt ? And am i right in my interpretation of what will happen during the process: the water will have some vertical speed which will reduced to zero as soon as it meets any bucket but it will instantly gain the speed of that bucket at that instant so its getting a force impulsive from the walls of the container which is varying with time?

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You are correct in the reasoning that the falling water will apply an impulsive force on the walls of the container and which will decrease the angular speed of rotation. The water from the tap is falling at a constant rate doesn't mean that it fills the entire bucket. It only says the total mass of water added to the buckets per unit time. It doesn't matter in which bucket the water falls as the moment of inertia depends on the distance of the mass from the axis of rotation and the distance is the same for all the buckets.

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  • $\begingroup$ I think problem says mass of water added to buckets per unit time is m not the bucket isnt? $\endgroup$ Commented Mar 26, 2022 at 5:18
  • $\begingroup$ I edited the sentence for clarity. Does it make more sense now? $\endgroup$ Commented Mar 26, 2022 at 5:23
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    $\begingroup$ Yeah thanks and it should be total mass of water added to buckets not just a bucket you may edit $\endgroup$ Commented Mar 26, 2022 at 5:25

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