Question

In a capillary tube experiment, a vertical 30 cm long capillary tube is dipped in water, water rises upto a height of 10 cm due to capillarity. If this experiment is conducted in a freely falling elevator, then the length of the water column becomes

• A. 10 cm
• B. 20 cm
• C. 30 cm
• D. Zero

Hint:

Remember that apparent weightlessness (free fall) implies $g_{eff} = 0$. In situations where a physical quantity is inversely proportional to $g$, a zero $g$ means the effect would theoretically be infinite, limited only by physical boundaries.

Answer 1

The Correct Option is C

Step 1: Understanding the Question:
The problem describes a capillary rise experiment performed on Earth and then asks what happens to the height of the water column if the same experiment is conducted in a freely falling elevator.
Step 2: Key Formula or Approach:
The height of capillary rise ($h$) is given by the Jurin's Law: \[ h = \frac{2T \cos\theta}{\rho g r} \] Where:
- \( T \) is the surface tension of the liquid.
- \( \theta \) is the contact angle.
- \( \rho \) is the density of the liquid.
- \( g \) is the acceleration due to gravity.
- \( r \) is the radius of the capillary tube.
Step 3: Detailed Explanation:
In a freely falling elevator, the apparent weight of objects inside becomes zero. This means the effective acceleration due to gravity ($g_{eff}$) inside the elevator is zero ($g_{eff} = g - a = g - g = 0$, where $a=g$ for free fall).
From Jurin's Law, the height of capillary rise ($h$) is inversely proportional to $g$: \( h \propto \frac{1}{g} \).
If $g_{eff} = 0$, then the height $h$ would theoretically become infinite. However, the water cannot rise beyond the length of the capillary tube.
Given that the capillary tube is 30 cm long, the water will rise to fill the entire length of the tube.
Step 4: Final Answer:
The length of the water column becomes 30 cm.