A barometer kept in an elevator accelerating upward reads 76 cm. The air pressure in the elevator is

Options

A. 76cm
B. lt76cm
C. gt76cm
D. zero

Answer

To solve the problem of determining the air pressure in an elevator that is accelerating upward and reads 76 cm on a barometer, we can follow these steps:

### Step 1: Understand the Barometer
A barometer measures atmospheric pressure by balancing the weight of a column of liquid (usually mercury) against the atmospheric pressure. The height of the mercury column (H) is directly related to the pressure exerted by the atmosphere.

### Step 2: Use the Barometric Formula
Under normal conditions, the atmospheric pressure (P) can be expressed as:
\[ P = \rho g H \]
where:
- \( P \) = atmospheric pressure,
- \( \rho \) = density of mercury (approximately \( 13,600 \, \text{kg/m}^3 \)),
- \( g \) = acceleration due to gravity (approximately \( 9.81 \, \text{m/s}^2 \)),
- \( H \) = height of the mercury column (in meters).

### Step 3: Adjust for Elevator Acceleration
When the elevator accelerates upward with an acceleration \( a \), the effective acceleration due to gravity becomes:
\[ g_{\text{effective}} = g + a \]
Thus, the pressure reading in the barometer when the elevator is accelerating upward will be:
\[ P' = \rho g_{\text{effective}} H \]
Substituting \( g_{\text{effective}} \):
\[ P' = \rho (g + a) H \]

### Step 4: Relate the Two Pressures
Given that the barometer reads 76 cm of mercury when the elevator is accelerating, we can equate this to the height in the formula:
\[ P' = \rho (g + a) (0.76 \, \text{m}) \]

### Step 5: Compare Pressures
The pressure inside the elevator (due to the upward acceleration) is greater than the normal atmospheric pressure. Therefore, we have:
\[ P' > P \]
Where \( P \) is the normal atmospheric pressure (which corresponds to 76 cm of mercury).

### Step 6: Conclusion
Since the barometer reads 76 cm in the accelerating elevator, the air pressure in the elevator is greater than the standard atmospheric pressure. Thus, we can conclude that the air pressure in the elevator is greater than the pressure corresponding to 76 cm of mercury.

### Final Answer
The air pressure in the elevator is greater than 76 cm of mercury.

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