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Pressure Due to Liquid Column

A sealed tank...

Question

A sealed tank containing a liquid of density moves with a horizontal acceleration $a$ as shown in the figure. Find the difference in pressure between the points A and B.

A

P_{B} - P_{A} = 5 h ρ g + ℓ ρ a

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B

P_{B} - P_{A} = h ρ g + ℓ ρ a

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C

P_{B} - P_{A} = 2 h ρ g + ℓ ρ a

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D

P_{B} - P_{A} = 3 h ρ g + ℓ ρ a

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Solution

The correct option is B $P_{B} - P_{A} = h ρ g + ℓ ρ a$

We know,
By drop and gain method,

$P_{A} + ρ l a + ρ g h = P_{B}$

$P_{B} - P_{A} = ρ l a + ρ g h$

Option $B$ is the correct answer.

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