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A cubical box is completely filled with mass m of a liquid and is given horizontal acceleration ‘a’ as shown. Match the force due to fluid pressure on the faces of the cube with their appropriate values (assume – zero pressure at minimum pressure)

List I List II
A) Force on face ABFE P) $\frac{m a}{2}$
B) Force on face BFHD Q) $\frac{m g}{2}$
C) Force on face ACGE R) $\frac{m a}{2} + \frac{m g}{2}$
D) Force on face CGHD S) $\frac{m a}{2} + m g$
T) $\frac{m g}{2} + m a$

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$A \to P; B \to Q; C \to R; D \to S$

$A \to Q; B \to P; C \to T; D \to S$

$A \to P; B \to Q; C \to S; D \to T$

$A \to P; B \to Q; C \to T; D \to S$

answer is D.

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Detailed Solution

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

$P_{a v e} = \frac{O + ρ l a}{2} = \frac{ρ l a}{2}$

$F_{A B F A} = P_{a v e} . A$

$= \frac{ρ l a}{2} . l^{2} = \frac{ρ l^{3} a}{2} = \frac{m a}{2}$

$P_{a v e} = \frac{O + ρ g l}{2} = \frac{ρ g l}{2}$

$F_{B F H D} = \frac{ρ g l}{2} . l^{2} = \frac{ρ l^{3} g}{2} = \frac{m g}{2}$

$F_{A C G E} = F_{s} + F_{g}$ $F_{b} \to Psudo force$

$= ρ l^{3} a + \frac{ρ l^{3} g}{2}$ $F_{g} \to gravity force$

$= m a + \frac{m g}{2}$

$F_{C G H D} = \frac{ρ l^{3} a}{2} + ρ l^{3} g$

$= \frac{m a}{2} + m g$

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List I	List II
A) Force on face ABFE	P) $\frac{m a}{2}$
B) Force on face BFHD	Q) $\frac{m g}{2}$
C) Force on face ACGE	R) $\frac{m a}{2} + \frac{m g}{2}$
D) Force on face CGHD	S) $\frac{m a}{2} + m g$
	T) $\frac{m g}{2} + m a$