A U-tube of horizontal arm length L (tube diameter d << L) is rotated about one of its vertical limbs with angular speed omega. Find the difference H in the liquid-column heights (liquid density rho) between the two limbs.

omega²*L²/(2g)
omega²*L²/g
omega²*L/(2g)
rho*omega²*L²/(2g)

Correct answer: omega²*L²/(2g)

Solution

Rotation raises the pressure (and hence column height) at the outer limb. The pressure difference between the axis limb and the outer limb supports the height difference H.

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