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’ and the walls of the vessel are inclined at an angle 30° with the vertical. A liquid of density ρ fills both the sections up to a height 2h. Neglecting atmospheric pressure.. Image
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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’ and the walls of the vessel are inclined at an angle 30° with the vertical. A liquid of density ρ fills both the sections up to a height 2h. Neglecting atmospheric pressure.. Image

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G1 Physics · Accepted Answer

Step 1: The base pressure is p = ρg(2h), so the upward force exerted by the base on the liquid is F = 2ρghA. Step 2: Because the upper vessel narrows upward, its volume is smaller than Ah; hence the liquid weight W is less than 2ρghA. The sloping walls must therefore exert a downward force F − W on the liquid. Correct answer: D.