Q:A light cylindrical vessel is kept on a horizontal surface. Its base area is A. A hole of cross sectional area ‘ a ‘ is made just at its bottom side. The minimum coefficient of friction necessary for sliding of the vessel due to the impact force of the emerging liquid is (a<< A)

(A) varying

(B) a/A

(C) 2a/A

(D) None of these

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The velocity of efflux of the liquid is given as

$ \displaystyle v= \sqrt{2 g y} $

The impact force of the emerging liquid on the vessel + liquid content is equal to

$ \displaystyle F = v\frac{dm}{dt} = v a \rho v = a\rho v^2 $

(since av = volume per sec & avρ = mass per sec )

$ \displaystyle F = a \rho (2 g y) = 2a\rho g y $

The force of friction = f = F = 2aρgy

μN = 2aρgy

μ(Aρgy) = 2a ρgy

μ = 2a/A