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Accelerating Containers

A sealed tank...

Question

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

h ρ g

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l ρ g

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h ρ g - l ρ a

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h ρ g + l ρ a

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Solution

The correct option is D $h ρ g + l ρ a$
The points A and C are in same horizontal level.
Hence, $P_{C} - P_{A} = ρ a l$
Now, $P_{B} - P_{C} = ρ g h$
$\Rightarrow P_{B} = (P_{A} + ρ a l) + ρ g h \Rightarrow P_{B} - P_{A} = h ρ g + l ρ a$

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