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Standard XII

Physics

Pressure

Two vessels A...

Question

Two vessels $A$ and $B$ of different shapes have the same base area and are filled with water upto the same height $h$ (as shown). The force exerted by water on the base is $F_{A}$ for vessel $A$ and $F_{B}$ for vessel $B$ . The respective weights of water in the vessels are $W_{A}$ and $W_{B}$ . Then

F_{A} > F_{B}; W_{A} > W_{B}

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F_{A} = F_{B}; W_{A} > W_{B}

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F_{A} = F_{B}; W_{A} < W_{B}

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F_{A} > F_{B}; W_{A} = W_{B}

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Solution

The correct option is B $F_{A} = F_{B}; W_{A} > W_{B}$
As we know,
$Force = Pressure \times Area$
and Pressure ( $P) = ρ g h$
Given, $ρ$ and $h$ are the same for both vessels.
Thus, $P_{A} = P_{B}$
Also given, base area is the same.
So, $F_{A} = F_{B}$

Weight of the liquid depends on the volume of liquid and density of liquid in the container.
$W = V \times ρ$
Here, we have the same liquid. Hence, density is the same for both liquids. But clearly, vessel $A$ contains more volume of liquid than vessel $B$ .
Hence, $W_{A} > W_{B}$

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Pressure

Standard XII Physics

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Two vessels A and B of different shapes have the same base area and are filled with water upto the same height h (as shown). The force exerted by water on the base is FA for vessel A and FB for vessel B. The respective weights of water in the vessels are WA and WB. Then