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The height of the Mercury column is not affected by the diameter of the tube.

Here is the proof:

Pressure is force per unit area; P =F/A. Force, F = mass (m) x gravity acceleration (g), and mass = density( d) x volume (V)

Therefore, P = (d x V x g) / A. Since volume (V) = Area (A) x height (h), then

P = (d x A x h x g) / A, which upon cancelling A from numerator and denominator gives P = d x h x g. This shows that diameter of the tube has no effect on height of mercury inside the barometer tube.

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