A 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 water in an elevator, then the length of the water column becomes

The height of capillary rise is given by \(h = \dfrac{2T \cos \theta}{\rho g_{eff} r}\)

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

Substituting \(g_{eff} = 0\) in the formula, the theoretical height \(h\) tends to infinity.

However, the water column cannot exceed the physical length of the capillary tube. Once the water reaches the top, the radius of curvature of the meniscus adjusts to prevent overflow.

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

Since the length of the capillary tube is \(30\) cm, the length of the water column becomes \(30\) cm.

Answer: \(30\) cm