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A mass M of liquid of density rho is poured into a light beaker placed on a horizontal table. The liquid stands to height h, and the beaker is wider at the top than at the base, with base cross-sectional area A. Ignoring atmospheric pressure, which statement(s) is/are correct?

1. The liquid pressure at the bottom surface is rho*g*h.
2. The normal reaction of the table on the beaker is rho*g*h*A.
3. The liquid pressure at the bottom surface is M*g/A.
4. The normal reaction of the table on the beaker is M*g.

Correct answer: The liquid pressure at the bottom surface is rho*g*h.

Solution

Pressure at the bottom is rho*g*h regardless of shape, so the first statement is correct. The normal reaction from the table supports the entire weight: N = M*g, so the fourth statement is also correct. The force on the base equals rho*g*h*A which is not M*g for a beaker wider at top (the slanted walls carry a downward share), so options about M*g/A pressure and rho*g*h*A reaction being the table reaction are wrong. The single best correct statement among these is that the bottom pressure is rho*g*h.

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