Water and Kerosine are drawn respectively into the two limbs of a Hare's apparatus. The destiny of water is…

Analysis

This problem involves the principle of a Hare's apparatus, which is used to compare the densities of two liquids. In this apparatus, the pressure exerted by the column of liquid in each limb must be equal at the level of the common interface (the bottom).

Concept

The pressure ($P$) exerted by a liquid column is given by the formula:

Where:

• $\rho$ (rho) = density of the liquid
• $g$ = acceleration due to gravity
• $h$ = height of the liquid column

Since both limbs are under the same atmospheric pressure and the pressure at the base of both columns is equal, we use the principle:

Where:

• $\rho_w$ = density of water
• $h_w$ = height of water
• $\rho_k$ = density of kerosine
• $h_k$ = height of kerosine

Solution

Step 1: Identify the given values.

• Density of water ($\rho_w$) = $1.0 \, \text{gcm}^{-3}$
• Height of water ($h_w$) = $20.0 \, \text{cm}$
• Density of kerosine ($\rho_k$) = $0.80 \, \text{gcm}^{-3}$
• Height of kerosine ($h_k$) = ?

Step 2: Substitute the values into the formula.

Step 3: Solve for $h_k$.

Conclusion

The height of the kerosine column is 25.0 cm.

Exam Tip

Always remember that in a Hare's apparatus, the liquid with the lower density must have a higher column to balance the pressure of the denser liquid. Since kerosine is less dense than water ($0.8 < 1.0$), you should expect your answer to be greater than 20.0 cm. If you get a smaller number, check your calculation!