Question

Water does not run out of a dropper unless its rubber bulb is pressed

Answer 1

The pressure in the dropper is equal to the pressure outside the dropper (atmospheric pressure). But as we press the rubber tube pressure inside increases. As liquid flows from a region of high pressure to low pressure it flows out. NOTE- If we press lightly only some water comes out this is because with some force applied on the rubber tube the pressure quickly becomes equal after some water has come out.

Answer 2

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