A large open container of negligible mass and area A has a side hole of area A/100 near the bottom. It contains liquid of density ρ and initial mass m₀ and can move frictionlessly on a horizontal floor. When outflow starts, find (i) the container acceleration and (ii) its speed when 75% of the liquid has drained.
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Question

A large open container of negligible mass and area A has a side hole of area A/100 near the bottom. It contains liquid of density ρ and initial mass m₀ and can move frictionlessly on a horizontal floor. When outflow starts, find (i) the container acceleration and (ii) its speed when 75% of the liquid has drained.

Options

G1 Physics · Accepted Answer

Step 1: Use continuity A₁v₁ = A₂v₂ and Bernoulli's equation P + ½ρv² + ρgh = constant; for jets use momentum flux ṁΔv. Step 2: Substitute the stated areas, levels and pressures, including Torricelli v = √(2gh) where applicable. Applying these relations to the given data gives A: (i) 0.2 m s⁻², (ii) √(m₀g/(2ρA)). Final answer: A.