The vessel shown in the figure has two sections of areas of cross section A1 and A2- A liquid of density - fills both the sections- upto a height h in each- Neglect atmospheric pressure-

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Byju's Answer

Standard XII

Physics

Pascal's Law

The vessel sh...

Question

The vessel shown in the figure has two sections of areas of cross section $A_{1}$ and $A_{2}$ . A liquid of density $ρ$ fills both the sections, upto a height h in each. Neglect atmospheric pressure.

The pressure at the base of the vessel is

2 h ρ g

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The force exerted by the liquid on the base of the vessel is

2 h ρ g A_{2}

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The weight of the liquid is <

2 h ρ g A_{2}

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The walls of the vessel at the level X exert a downward force

h ρ g (A_{2} - A_{1})

on the liquid

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Solution

The correct options are
A The pressure at the base of the vessel is $2 h ρ g$
B The force exerted by the liquid on the base of the vessel is $2 h ρ g A_{2}$
C The weight of the liquid is < $2 h ρ g A_{2}$
D The walls of the vessel at the level X exert a downward force $h ρ g (A_{2} - A_{1})$ on the liquid
Pressure at the bottom $= ρ g Δ H = 2 ρ g h$
Force at bottom $= 2 ρ g h \times A_{2}$
Weight of liquid is less than $2 ρ g h \times A_{2}$
$Δ F = ρ g h A_{2} - ρ g h A_{1} = ρ g h {(A}_{2} - A_{1})$

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The vessel shown in the figure has two sections of areas of cross section A1 and A2. A liquid of density ρ fills both the sections, upto a height h in each. Neglect atmospheric pressure.

The vessel shown in the figure has two sections of areas of cross section $A_{1}$ and $A_{2}$ . A liquid of density $ρ$ fills both the sections, upto a height h in each. Neglect atmospheric pressure.