A capillary tube 20 cm long is dipped in water, causing the water...

The height of capillary rise is given by the formula:

$h = \dfrac{2T \cos \theta}{\rho r g_{\text{eff}}}$

In a freely falling elevator, the effective acceleration due to gravity is zero ($g_{\text{eff}} = 0$).

As $g_{\text{eff}} \rightarrow 0$, the theoretical height $h \rightarrow \infty$. However, the liquid cannot overflow from the upper end of the capillary tube. Instead, the liquid rises to the top of the tube and the meniscus adjusts its radius of curvature $R$ such that $h R = \text{constant}$.

Thus, the water will rise to the full length of the capillary tube.

Since the total length of the capillary tube is $20 \text{ cm}$, the length of the water column will be $20 \text{ cm}$.