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A cylindrical vessel filled with water u...

A cylindrical vessel filled with water up to a height of `2 m` stands on a horizontal plane. The side of the vessel has a plugged circular hole so that the vessel begins to move on the floor it the plug is removed. The coefficient of friction between the bottom of the vessel and the plane is `0.4`, and total mass of water plus vessel is `100 kg`.

Text Solution

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From torricelli's theorem, velocity of efflux `=(2gh)`
Momentum per second carried by water stream (efflux)
`=` density `xx`volume coming out per second `xx` velocity `=rhoxxavxxv=rhoav^(2)`
Hence force on cylinderical cessel `=rhoa2gh`
Cylinder starts to move when reaction force is just equal to maximum force of friction i.e.,
`muMg=rhoa2ghimpliesa=(muM)/(2rhoh)=(0.4xx100)/(2xx10^(3)xx2)=0.01m^(2)`
Area of circular hole `=(pid^(2))/(4)=0.01m^(2)impliesd=sqrt((0.01xx4)/(pi))=0.113`m
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