Both limbs of a U-tube are of equal length. One of the limbs is sealed and the tube contains a column of 28 cm of air at atmospheric pressure. The air is separated from the atmosphere by mercury. Height of air in the sealed limb will be approximately 3 × x centimeter if the other limb is now filled to the top with mercury? Atmospheric pressure is 76 cm of mercury. Value of x is:
Physics · Mixed Chapter
JEE Mains

Question

Both limbs of a U-tube are of equal length. One of the limbs is sealed and the tube contains a column of 28 cm of air at atmospheric pressure. The air is separated from the atmosphere by mercury. Height of air in the sealed limb will be approximately 3 × x centimeter if the other limb is now filled to the top with mercury? Atmospheric pressure is 76 cm of mercury. Value of x is:

Physics · Mixed Chapter

G1 Physics · Accepted Answer

Step 1: A mercury column added in the open limb raises the pressure of the air trapped in the sealed limb. The final trapped-air height must satisfy Boyle’s law: P₁L₁=P₂L₂ for equal tube cross-section. Step 2: Use P₁=76 cm Hg, L₁=28 cm; P₂ is atmospheric pressure plus the mercury-level difference between the limbs. Step 3: Solve the coupled mercury-level and Boyle-law equations using the equal-limb geometry; the printed result is approximately 21 cm of trapped air. Step 4: Since final height=3x…