JEE Main · 2021 · 27 Jul 2021 · Shift 1 · Fluid Mechanics

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A light cylindrical vessel is kept on a horizontal surface. Area of base is A. A hole of cross-sectional area 'a' is made just at its bottom side. The minimum coefficient of friction necessary to prevent sliding the vessel due to the impact force of the emerging liquid is

(a ≪ A)

(A)None of these
(B) $\frac{2 a}{A}$ ✓ Correct
(C) $\frac{A}{2 a}$
(D) $\frac{a}{A}$

Answer: (B)

Solution

The velocity of efflux is

v = 2 g h

. The thrust force on the vessel is

F = v \frac{d m}{d t} = a ρ v^{2} = 2 a ρ g h

. The friction force is

f_{r} = μ R = μ A h ρ g

. For the vessel to just not slide,

f_{r} = F

, giving

μ A h ρ g = 2 a ρ g h

. Therefore,

μ = \frac{2 a}{A}

JEE Main · 2021 · 27 Jul 2021 · Shift 1 · Single correct option

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