A water-filled pond has the shape of an inverted truncated cone and depth 30 m. Atmospheric pressure above the water is 1.0 × 10⁵ Pa. The top and bottom circular surfaces have radii R₂ and R₁, respectively. The magnitude of the force on the top surface by the atmosphere equals the magnitude of the force on the bottom surface by the liquid. Find R₂/R₁. Image
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Question

A water-filled pond has the shape of an inverted truncated cone and depth 30 m. Atmospheric pressure above the water is 1.0 × 10⁵ Pa. The top and bottom circular surfaces have radii R₂ and R₁, respectively. The magnitude of the force on the top surface by the atmosphere equals the magnitude of the force on the bottom surface by the liquid. Find R₂/R₁. Image

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G1 Physics · Accepted Answer

Step 1: Pressure at the top surface is Ptop = 1.0×10⁵ Pa. At 30 m depth, Pbottom = Ptop + ρgh = 1.0×10⁵ + 1000×10×30 = 4.0×10⁵ Pa. Step 2: Equal forces give PtopπR₂² = PbottomπR₁². Therefore (R₂/R₁)² = 4 and R₂/R₁ = 2. Correct answer: A.