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Suppose I have an oil drop which is negatively charged placed in a box with the bottom of the box negatively charged. When this box and oil drop is placed on a table where the box is stationary, the oil drop is stationary in the middle of the box. Hence, we can conclude that the force of repulsion between the negatively charged oil drop and bottom surface of the box is EQUAL to the the weight.

So now, I drop the whole system from the top of a building. Assume there is no air resistance. Since the whole system is in free fall, is it correct to say that for the same oil drop and box, the oil drop will now move upwards towards the top of the box?

Since free fall is the same as being in outer space with zero gravity.

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    $\begingroup$ Can you think of any reasons why that might not be true? $\endgroup$
    – PM 2Ring
    May 25, 2021 at 1:56
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    $\begingroup$ A related question (relative to MP 2Ring): if the droplet was in static equilibrium before you dropped the box, what do you expect when the force of gravity is suddenly removed from the free body diagram? $\endgroup$ May 25, 2021 at 2:29
  • $\begingroup$ I mean nothing unique about oil droplets here. If you drop a bottle of water the distribution of water inside the bottle will shift upward $\endgroup$
    – Señor O
    May 25, 2021 at 4:13
  • $\begingroup$ So this is true right? Just making sure because I was having a debate with my friend and he said the otherwise. $\endgroup$ May 25, 2021 at 5:08
  • $\begingroup$ he said the otherwise because both the box and the oil drop is moving together so nothing will change. $\endgroup$ May 25, 2021 at 5:28

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Simple answer is, the oil droplet will slowly move upwards. Because, the oil droplet is floating in the middle of the box for electrostatic repulsion. 'The droplet can't start it's free fall until the box's surface or the box move downwards'— What does it mean? It means that that box starts it's free fall before the oil droplet;and so the box gains a higher velocity than the droplet due to gravitational acceleration. And if the box gains a higher velocity than the droplet, the droplet will start going upwards in the box.

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