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 sdie (where a ltlt A). Find minimum coefficeint of friction necessary for sliding of the vesssel due to the impact force of the emerging liquid.

Explanation

Let h be the height of liquid in vessel above the hole.
Velocity of efflux, `upsilon = sqrt(2 gh)`
Impact force of the emerging liquid on the vessel and liquid contents is
`F = upsilon (dm)/(dt) = upsilon(a rho upsilon) = a rho upsilon^(2) = a rho 2 gh = 2 arho gh` The force of friction, `f = mu R = muA h rho g` For just sliding the vessel, f =f So, `mu A h rhog = 2 a rho gh or mu = (2a)/(A)`