Question

A uniform narrow tube of length one metre with one end closed contains 25 cm long mercury thread, which traps a column of air at the closed end. When the tube is held vertically with the open end up, the length of the air column near the closed end is 21 cm and when the tube is held horizontally, the length of the air column near the closed end is ‘L’. If the atmospheric pressure is equal to the pressure of 75 cm of mercury, then \( L \) is:

• A. \( 35 \, \text{cm} \)
• B. \( 28 \, \text{cm} \)
• C. \( 7 \, \text{cm} \)
• D. \( 14 \, \text{cm} \)

Hint:

When a liquid column is in a tube, the length of the air column at equilibrium depends on the pressure and the height of the liquid column.

Answer 1

The Correct Option is B

Step 1: The pressure at the closed end of the tube is given by: \[ P = \text{atmospheric pressure} + \text{pressure due to mercury column} \] 

Step 2: When the tube is held vertically, the pressure at the closed end is \( 75 \, \text{cm} \) of mercury. 

Step 3: When the tube is held horizontally, the length of the air column changes due to the balance of pressures. The total length of the column is \( L = 28 \, \text{cm} \).