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

Column-I Column-II
a) The net force exerted by liquid on side walls is p) $2 h ρ g A_{2}$
b) The force exerted by the liquid on the base of the vessel is q) Zero
c) The weight of the liquid in vessel r) $h ρ g (A_{2} - A_{1})$
d) The walls of the vessel at the level X exert a downward force is s) Less than $2 h ρ g A_{2}$

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$a \to p, b \to s, c \to q, d \to r$

$a \to q, b \to p, c \to s, d \to r$

$a \to s, b \to r, c \to q, d \to p$

$a \to r, b \to q, c \to s, d \to p$

answer is B.

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Detailed Solution

Pressure at bottom of vessel
   $P = 2 ρ g h$
Force on bottom of vessel
$F = 2 ρ g h_{} A_{2}$
Force exerted by vessel at level x on liquid is    $F = h ρ g (A_{2} - A_{1})$

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