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

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

$<b> P₂ - P₁ = ρla</b>$

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.

$<b>Therefore, In the Given case,</b>$

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

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

$<b>P₂ - P₁ = hρg</b>$

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

$<b>Equation both the equation,</b>$

   hρg = ρla₀

   hg = la₀

∴ h = la₀/g

$<b>$Hence, the difference in heights of the liquid in two arms is la₀/g.

Hope it helps.