Question

A U-tube containing a liquid is accelerated horizontally with a constant acceleration a₀. If the separation between the vertical limbs is l, find the difference in the heights of the liquid in the two arms.

Answer 1

When any liquid is accelerated with an acceleration, then the pressure difference is given by the Formula,

 P₂ - P₁ = ρla

where ρ is the density of the fluid, and l is the distance between two vertical limbs of the container and a is the acceleration.

Therefore, In the Given case,

   P₂ - P₁ = ρla₀    [∵ a₀ is the acceleration is horizontal direction.]

Now, We know, Pressure difference has one more formula,

P₂ - P₁ = hρg

where ρ is the density of the fluid and h is the height difference between a pressure P₂ and Pressure P₁.

Equation both the equation,

   hρg = ρla₀

   hg = la₀

∴ h = la₀/g

Hence, the difference in heights of the liquid in two arms is la₀/g.

Hope it helps.