A tube of length L is filled completely with an incompressible

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A tube of length L is filled completely with an incompressible liquid of mass M and closed at both the ends. The tube is then rotated in a horizontal plane about one of its ends with a uniform angular velocity ω. The force exerted by the liquid at the other end is

1. ML²ω
  2
2. ML²ω²
3. ML²ω²
  2
4. MLω²
  2

Correct Option: D

Rotation will create centrifugal force due to which pressure will be created at the other end. Now, this centrifugal force will depend on distance of the liquid from the axis as centrifugal force = mω²r.
Let us consider a small part dx of the liquid column which is at a distance of x. Let linear density of liquid be ρ.
Mass of the liquid in dx length = dx . A. ρ
(A is cross sectional area of tube)
Centrifugal force = dxAρ × ω²x
Centrifugal force due to whole of liquid length

⇒ Aρ	ω²L²	= AL	ρω²L	=	MLω²
	2		2		2

ML²ω
2

ML²ω²
2