1.

A light clindrical vessel is kept on a horizontal surface. The base are is A. A hole of cross-sectional area a is made just at its bottom side (where alt ltA) fig. Find minimum coeffiecent of friction necessary for sliding of the vessel due to the impact of the emerging liquid.

Answer» Let h be the height of liquid in vessel above the hole.
Velocity of efflux, `upsilon = sqrt(2 gh)`
Impact force of the imerging 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 a rho gh `
The force of friction, `f = mu R =mu A h rho g`
For just sliding the vessel , `f =F`
so, `mu A h rho g = 2 a rho g h or mu = (2a)/(A)`.


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