A barometer kept in a stationary elevator reads `76 cm`. If the element starts accelerating up the reading will be

Options

A. Zero
B. Equal to `76 cm`
C. More than `76 cm`
D. Less than `76 cm`

Answer

To solve the problem of how the reading of a barometer changes when an elevator accelerates upwards, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding the Initial Condition**:
- The barometer reads 76 cm of mercury when the elevator is stationary. This reading corresponds to the atmospheric pressure at that location.

2. **Effect of Upward Acceleration**:
- When the elevator starts to accelerate upwards, the effective gravitational acceleration experienced by the barometer increases. This is because the barometer measures the pressure exerted by the column of mercury, which is influenced by both the gravitational pull and the upward acceleration of the elevator.

3. **Calculating Effective Acceleration**:
- Let \( g \) be the acceleration due to gravity (approximately \( 9.81 \, \text{m/s}^2 \)).
- Let \( a \) be the upward acceleration of the elevator.
- The effective gravitational acceleration \( g_{\text{effective}} \) when the elevator accelerates upwards is given by:
\[ g_{\text{effective}} = g + a \]

4. **Pressure Relation**:
- The pressure exerted by a column of liquid is given by the formula:
\[ P = \rho g h \]
- Where \( P \) is the pressure, \( \rho \) is the density of the liquid (mercury in this case), \( g \) is the acceleration due to gravity, and \( h \) is the height of the liquid column.

5. **Finding the New Height**:
- When the elevator accelerates upwards, the pressure exerted by the mercury column must balance the atmospheric pressure. Therefore, we can set up the equation:
\[ P_{\text{atm}} = \rho g_{\text{effective}} h' \]
- Where \( h' \) is the new height of the mercury column when the elevator is accelerating.
- Rearranging gives:
\[ h' = \frac{P_{\text{atm}}}{\rho g_{\text{effective}}} \]

6. **Comparing Heights**:
- Since \( g_{\text{effective}} = g + a \), we can see that as \( g_{\text{effective}} \) increases, \( h' \) will decrease because \( h' \) is inversely proportional to \( g_{\text{effective}} \).
- Thus, the new height \( h' \) will be less than the original height of 76 cm.

7. **Conclusion**:
- Therefore, when the elevator accelerates upwards, the reading of the barometer will decrease from 76 cm.

### Final Answer:
The reading of the barometer will be less than 76 cm when the elevator accelerates upwards.