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Floating

The vessel sh...

Question

The vessel shown in the figure has two sections. The lower part is a rectangular vessel with area of cross-section $A$ and height $h$ . The upper part is a conical vessel of height $h$ with base area ' $A$ ' and top area ' $a$ ' ad the walls of the vessel are inclined at an angle $30^{\circ}$ with the vertical. A liquid of density $ρ$ fills both the sections upto a height $2 h$ . Neglecting atmospheric pressure.

The force

F

exerted by the liquid on the base of the vessel is

2 h ρ g \frac{(A + a)}{2}

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the pressure

P

at the base of the vessel is

2 h ρ g \frac{A}{a}

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the weight of the liquid

W

is greater than the force exerted by the liquid on the base

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the walls of the vessel exert a downward force

(F - W)

on the liquid

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Solution

The correct option is D the walls of the vessel exert a downward force $(F - W)$ on the liquid
$F = ρ g 2 h A$
Pressure at bottom is $P = ρ g 2 h$
Weight of liquid is $W = ρ g (2 A h - (A - a) h / 2) = ρ g (3 A h / 2 + a h / 2)$
We can clearly see $F > W$
Downward forces due to wall is excess forces apart from weight $= F - W$

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The correct option is D the walls of the vessel exert a downward force (F−W) on the liquidF=ρg2hAPressure at bottom is P=ρg2hWeight of liquid is W=ρg(2Ah−(A−a)h/2)=ρg(3Ah/2+ah/2)We can clearly see F>WDownward forces due to wall is excess forces apart from weight =F−W