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Pressure

The A, B, and...

Question

The A, B, and C vessels are filled with the liquid of the same height. The bottom area of A is equal to the bottom area of B and is less than the bottom area of C.
Which of the following relation is correct for the value of the force at the bottom?
( $F_{A}, F_{B} and F_{C}$ are the force values at the bottom for A, B and C respectively.)

F_{A} = F_{B} = F_{C}

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F_{A} > F_{B} > F_{C}

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F_{A} < F_{B} < F_{C}

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F_{A} = F_{B} < F_{C}

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Solution

The correct option is D $F_{A} = F_{B} < F_{C}$
The height of the liquid is equal in all the containers, hence the pressure exerted at the bottom will be the same for all.

From defintion of pressure,
$Force = Pressure \times Area$
For the same pressure, the force increases as the area increases.
Given, the area of the bottom A is equal to the area of the bottom B and the area of the bottom C is greater than the area of the bottom A and B.
So the correct relation is $F_{A} = F_{B} < F_{C}$ .

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