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The height of a mercury barometer is h when the atmospheric pressure is 100,000 Pa. At height h/5, what is the pressure?

The choices given are

  1. 20,000
  2. 80,000
  3. 120,000
  4. 180,000

The answer given is:

Pressure at height h/5 = (h-h/5) of Mercury = (4/5)*100,000 Pa = 80,000 Pa.

Why h-h/5? I think it should be (1/5)*100,000=20,000?

Then there is a note below the answer that says

The pressure of liquid is proportional to the depth of liquid.

I understand that but do not understand why it must be 4/5 of 100,000.

So at height 4h/5, the pressure is 20,000 Pa?

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closed as off-topic by John Rennie, yuggib, Martin, Qmechanic Jun 26 '15 at 11:36

This question appears to be off-topic. The users who voted to close gave this specific reason:

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If this question can be reworded to fit the rules in the help center, please edit the question.

  • $\begingroup$ @ACuriousMind Oh thanks for the edit. I foolishly assumed the no homework tag applied to the whole SE rather than just Math SE meta.math.stackexchange.com/q/16425 $\endgroup$ – BCLC Jun 11 '15 at 12:32
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    $\begingroup$ At height h/5, the distance to the bottom is h/5, and the distance to the top is 4h/5. The note means the pressure is proportional to the distance from your position to the top. $\endgroup$ – mmesser314 Jun 11 '15 at 13:31
  • $\begingroup$ @mmesser314 Ah so the pressure of 100,000 is at height 0? $\endgroup$ – BCLC Jun 11 '15 at 13:39
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    $\begingroup$ Yes. Depth = h, and height = 0 at the bottom. $\endgroup$ – mmesser314 Jun 11 '15 at 13:41
  • $\begingroup$ @mmesser314 Thanks! Post as answer maybe? $\endgroup$ – BCLC Jun 11 '15 at 13:47
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At height h/5, the distance to the bottom is h/5, and the distance to the top is 4h/5. The note means the pressure is proportional to the distance from your position to the top.

So depth = h, and height = 0 at the bottom.

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