A rotating U-tube has horizontal arm L=1 m and vertical arms a=1 m. Liquid density ρ=10³ kg/m³ and initial air pressure P₀=10⁵ N/m². Right arm is sealed and becomes filled with liquid to y=1/2 m when the tube rotates about the left arm at ω=√(40/3) rad/s. Find sealed pressure in units of 10⁵ N/m².
Physics · Mixed Chapter
JEE Main Practice

Question

A rotating U-tube has horizontal arm L=1 m and vertical arms a=1 m. Liquid density ρ=10³ kg/m³ and initial air pressure P₀=10⁵ N/m². Right arm is sealed and becomes filled with liquid to y=1/2 m when the tube rotates about the left arm at ω=√(40/3) rad/s. Find sealed pressure in units of 10⁵ N/m².

Physics · Mixed Chapter

G1 Physics · Accepted Answer

Step 1: For a fluid rotating rigidly, ∂p/∂r=ρω²r; radial pressure rise over arm L is Δp_rot=½ρω²L². Step 2: Vertical pressure changes by ρgΔz. The sealed air also obeys pV=constant if temperature is fixed. Step 3: The source prints sealed pressure 1×10⁵ N/m². Reproducing it requires the initial trapped-air column and exact locations of the liquid levels, which the source graphic does not fully label. Step 4: Keep key 1, flagged for diagram-based review.