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Step-by-Step Solution
Step 1: State the phenomenon of capillary rise
When a capillary tube is dipped in water, the water rises in the tube due to surface tension and adhesive forces between the liquid and the walls of the tube. Normally, the height of the liquid column is governed by the balance between these forces and the effect of gravity.
Step 2: Recall how free fall affects gravitational acceleration
Inside a freely falling elevator, the effective gravitational acceleration $g$ becomes zero. In other words, everything inside the elevator experiences weightlessness because the system is in free fall.
Step 3: Apply zero effective gravity to capillary action
The usual formula for the height of the liquid column in a capillary tube is
$ h = \dfrac{2\gamma \cos\theta}{\rho \, g \, r} $,
where $\gamma$ is the surface tension, $\theta$ is the contact angle, $\rho$ is the density of the liquid, and $r$ is the radius of the tube. Under normal gravity, this determines the finite height of the water column (which was 8 cm in the given scenario).
However, if $g = 0$, then the resistance to the upward pull of water by surface tension is removed. As a result, the water can rise until it fills the entire capillary tube.
Step 4: Conclude the final height of water in the tube
Because the entire system is in free fall and thus the effective gravity is zero, the water will completely fill the capillary tube. As the tube is 20 cm long, the final length of the water column in the tube will be 20 cm.
Final Answer
20 cm
