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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Ans: (c)
Sol: 
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