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A cylindrical vessel with a very large cross-sectional area of 1000 cm² contains two immiscible liquids: the upper layer has density rho1 = 600 kg/m³ and the lower layer has density rho2 = 1200 kg/m³, as shown. A small horizontal hole of area 5 * 10⁻⁴ m² is present in the side wall. Identify the CORRECT statement(s): (A) If the surface is smooth, a rightward horizontal force of magnitude 4 N must be applied on the vessel to maintain its equilibrium. (B) If the surface is smooth, a rightward horizontal force of magnitude 3 N must be applied on the vessel to maintain its equilibrium. (C) If the surface is rough (mu = 0.04), the minimum horizontal force needed to maintain equilibrium is zero. (D) If the surface is rough (mu = 0.04), the maximum horizontal force needed to maintain equilibrium is 19.8 N.
- If the surface is smooth, a rightward horizontal force of magnitude 4 N must be applied on the vessel to maintain its equilibrium.
- If the surface is smooth, a rightward horizontal force of magnitude 3 N must be applied on the vessel to maintain its equilibrium.
- If the surface is rough (mu = 0.04), the minimum horizontal force needed to maintain equilibrium is zero.
- If the surface is rough (mu = 0.04), the maximum horizontal force needed to maintain equilibrium is 19.8 N.
Correct answer: If the surface is rough (mu = 0.04), the minimum horizontal force needed to maintain equilibrium is zero.
Solution
The jet thrust is about 4 N (directed leftward on the vessel); on a smooth surface a 4 N rightward force is needed (A correct). With mu = 0.04 and total weight large enough, friction alone can balance the 4 N thrust, so minimum applied force = 0 (C correct), while the maximum needed (when friction reverses) is thrust + mu*Weight (D gives 19.8 N). The most consistently derivable correct individual statement is C.
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