Question

A U tube containing a liquid moves with a horizontal acceleration along a direction joining the two vertical limbs. The separation between these limbs is d. Find the difference in their liquid levels.

(1) (h₁ - h₂)g / a

(2) (h₁ -h₂)a / g

(3) (h₁ + h₂)g / a

(4) (h₁ + h₂)a / g

Answer 1

Correct Answer is: (1) (h₁ - h₂)g / a

Let A be the area of cross-section of the U tube and ρ be the density of the liquid of U tube. Mass of the liquid in portion CD of U tube = A d ρ. As the U tube is moving with acceleration a, therefore putting force on liquid in the portion CD of U tube, F = mass × acceleration = A d ρ a (pseudo force)

Pressure of liquid at C = h₁ρg

Pressure of liquid at D = h₂ρg

Net force to the left on CD

= (h₁ρg – h₂ρg) A

So, (h₁ – h₂) ρg A = Adρa

or h₁ – h₂ = da/g.

d = (h₁– h₂) g/a