The vertical limbs of a U shaped tube are filled with a liquid of density ρ up to a height h on each side. The horizontal portion of the U tube having length 2h contains a liquid of density 2ρ. The U tube is moved horizontally with an acceleration g/2 parallel to the horizontal arm. The difference in heights in liquid levels in the two vertical limbs at steady state is nh/7. Find n.
Physics · Mixed Chapter
JEE Mains

Question

The vertical limbs of a U shaped tube are filled with a liquid of density ρ up to a height h on each side. The horizontal portion of the U tube having length 2h contains a liquid of density 2ρ. The U tube is moved horizontally with an acceleration g/2 parallel to the horizontal arm. The difference in heights in liquid levels in the two vertical limbs at steady state is nh/7. Find n.

Physics · Mixed Chapter

G1 Physics · Accepted Answer

Step 1: Analyze the fluid in the accelerated frame with effective body-force components g vertically down and a=g/2 horizontally opposite the motion. Step 2: Hydrostatic balance for a liquid element is dp=ρ(g dy+a dx), with each liquid's own density. Pressure must be continuous at both liquid interfaces. Step 3: The two immiscible liquids can shift their interfaces when acceleration is applied, so pressure balance must account for the resulting heights and horizontal segments as well as total-v…