To construct a barometer, a tube of length 1m is filled completely with mercury and is inverted in a mercury cup. The barometer reading on a particular day is 76 cm. Suppose a 1m tube is filled with mercury up to 76 cm and then closed by a cork. It is inverted in a mercury cup and the cork is removed. It is inverted in a mercury column in the tube over the surface in the cup will be

Options

A. zero
B. 76 cm
C. `gt 76` cm
D. `lt 76` cm

Answer

To solve the problem, we need to analyze the behavior of the mercury in the tube when it is inverted in the mercury cup after being filled to a height of 76 cm. Here’s a step-by-step solution:

### Step 1: Understand the initial setup
We have a 1-meter long tube filled with mercury up to 76 cm and closed with a cork. When this tube is inverted into a mercury cup and the cork is removed, we need to determine the height of the mercury column that will be formed in the tube.

**Hint:** Remember that the atmospheric pressure supports the mercury column in the barometer.

### Step 2: Analyze the pressure at the open end of the tube
When the cork is removed, the pressure at the open end of the tube (which is in contact with the atmosphere) is equal to the atmospheric pressure. This pressure will act on the mercury column inside the tube.

**Hint:** Atmospheric pressure is typically around 76 cm of mercury at sea level.

### Step 3: Determine the height of the mercury column
Since the tube is initially filled with mercury up to 76 cm, and the atmospheric pressure can support a mercury column of 76 cm, when the cork is removed, the mercury will not fall below the 76 cm mark. The mercury will remain at this height because the atmospheric pressure is equal to the weight of the mercury column.

**Hint:** Consider the balance of forces acting on the mercury column.

### Step 4: Conclude the height of the mercury column
Therefore, when the cork is removed, the mercury will stay at the same height of 76 cm in the tube. The remaining part of the tube (from 76 cm to 1 m) will be filled with air, but the mercury will not rise or fall beyond this point due to the balance of atmospheric pressure.

**Hint:** The height of the mercury column is determined by the atmospheric pressure, which is why it remains at 76 cm.

### Final Answer
The height of the mercury column in the tube over the surface in the cup will be **76 cm**.