College

What is the density of the other fluid in the barometer?

The height of mercury in an open barometer is 69 cm. The height of another fluid in the same barometer is 176 cm.

Answer :

To solve the problem of finding the density of another fluid in the barometer, we can use the concept of pressure equilibrium. Here's a step-by-step approach:

1. Understanding the Principle:
- In a barometer, the pressure exerted by the mercury column is equal to the pressure exerted by the other fluid column when they are in equilibrium and open to the same atmospheric pressure.
- The pressure exerted by a fluid column is given by the product of its height, density, and gravitational acceleration (Pressure = Height x Density x g), where g is a constant (acceleration due to gravity).

2. Given Data:
- Height of mercury column = 69 cm
- Height of the other fluid column = 176 cm
- Density of mercury = 13.6 g/cm³ (this is a known value and is consistent for mercury)

3. Using Pressure Equilibrium:
- Since the pressures are equal, we have:
[tex]\[
\text{Pressure by mercury} = \text{Pressure by the other fluid}
\][/tex]
- Writing in terms of height and density:
[tex]\[
\text{Height of mercury} \times \text{Density of mercury} = \text{Height of fluid} \times \text{Density of fluid}
\][/tex]

4. Calculating Density of the Other Fluid:
- Rearranging the formula to solve for the density of the other fluid:
[tex]\[
\text{Density of fluid} = \frac{\text{Height of mercury} \times \text{Density of mercury}}{\text{Height of fluid}}
\][/tex]
- Plugging in the given values:
[tex]\[
\text{Density of fluid} = \frac{69 \, \text{cm} \times 13.6 \, \text{g/cm}^3}{176 \, \text{cm}}
\][/tex]
- Simplifying this expression gives us the density of the fluid:
[tex]\[
\text{Density of fluid} \approx 5.33 \, \text{g/cm}^3
\][/tex]

So, the density of the other fluid in the barometer is approximately 5.33 g/cm³.