A glass tube `80 cm` long and open ends is half immersed in mercury. Then the top of the tube is closed and it is taken out of the mercury. A column of murcury `20 cm` long then remains in the tube. The atmospheric (in cm of Hg) is
(assume temperature to be constant )

Options

A. 75
B. 30
C. 60
D. 90

Answer

To solve the problem step by step, let's analyze the situation described:

1. **Understanding the Setup**:
- We have a glass tube that is 80 cm long, and it is half immersed in mercury. This means that 40 cm of the tube is submerged in mercury, while the other 40 cm is above the mercury level.
- When the tube is closed at the top and removed from the mercury, we are told that a column of mercury 20 cm long remains in the tube.

2. **Initial Conditions**:
- When the tube is half immersed in mercury, the pressure at the bottom of the tube (where it is submerged) is equal to the atmospheric pressure plus the pressure due to the mercury column above it.
- The height of the mercury column in the tube when it is immersed is 40 cm (the submerged part), and the pressure exerted by this column can be calculated using the formula:
\[ P = \rho g h \]
- Here, \( \rho \) is the density of mercury, \( g \) is the acceleration due to gravity, and \( h \) is the height of the mercury column (40 cm).

3. **Taking the Tube Out of Mercury**:
- After closing the top of the tube and removing it from the mercury, the pressure inside the tube will remain constant because the air inside the tube does not escape.
- The column of mercury that remains in the tube is now 20 cm long.

4. **Calculating the Atmospheric Pressure**:
- The atmospheric pressure can be represented as:
\[ P_0 = P_{inside} + P_{mercury} \]
- The pressure inside the tube (when closed) is equal to the pressure exerted by the remaining mercury column (20 cm) plus the pressure due to the air column above it.
- The total height of the mercury column when the tube is half immersed is 40 cm, and when taken out, we have 20 cm remaining. Therefore, the atmospheric pressure can be calculated as:
\[ P_0 = \rho g (h_{initial} + h_{remaining}) = \rho g (40 \, \text{cm} + 20 \, \text{cm}) = \rho g (60 \, \text{cm}) \]

5. **Final Answer**:
- The atmospheric pressure in cm of mercury is 60 cm.

Thus, the atmospheric pressure is **60 cm of Hg**.