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)

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

Solution :
Fluid Mechanics

The velocity of efflux of the liquid is given as
v =√2gy
 The impact force of the emerging liquid on the vessel + liquid content is equal to
F = v dm/dt = vaρv = aΡv²
 F = aρ(2gy) = 2aρgy
The force of friction = f = F = 2aρgy
 μN = 2aρgy  
μ(Aρgy) = 2a ρgy
 μ = 2a/A