A liquid of density ρ is filled in a U-tube is accelerated with an acceleration a so that the height of liquid in its two vertical arms are h 1 and h 2 as shown in the figure. If l is the length of horizontal arm of the tube, the acceleration a is

Question

A liquid of density ρ is filled in a U-tube is accelerated with an acceleration a so that the height of liquid in its two vertical arms are h 1 and h 2 as shown in the figure. If l is the length of horizontal arm of the tube, the acceleration a is, g ( h 1 - h 2 ) 2 l towards right, g ( h 1 - h 2 ) 2 l towards left, g ( h 1 - h 2 ) l towards right, g ( h 1 - h 2 ) l towards left

MARKS App · Accepted Answer

Pressure on left end of horizontal tube, p 1 = p 0 + h 1 ρ g Pressure on right end of horizontal tube, p 2 = p 0 + h 2 ρ g As p 1 > p 2 , so acceleration should be towards right hand side. If A is the area of cross-section of the tube in the horizontal portion of U-tube, then p 1 A - p 2 A = ( l A ρ ) a Or h 1 - h 2 ρ g A = l A ρ a a = g ( h 1 − h 2 ) l

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