Question

A 20 cm long capillary tube is dipped in water. The water rises up to 8 cm. If the entire arrangement is put in a freely falling elevator, the length of the water column in the capillary tube will be:
A) zero
B) 8 cm
C) 4 cm
D) 20 cm

Answer 1

Hint : We need to use the formula for the rise of water in a capillary tube. There we can substitute the value of the acceleration due to gravity with the net acceleration of the water in the tube under free fall to get the answer.

Formula used: In this solution, we will use the following formula:
 $\Rightarrow h={\displaystyle \frac{2T\cos \theta }{r\rho g}}$ where $h$ is the rise in height of the liquid inside the capillary, $T$ is the tension in the liquid and $\rho$ is the density of the liquid, $\theta$ is the angle of contact, and $g$ is the gravitational acceleration acting on the object.

Complete step by step answer
When a capillary tube is dipped in water, the water rises inside the capillary tube. The height of the rise of the water inside the tube is calculated as:
 $\Rightarrow h={\displaystyle \frac{2T\cos \theta }{r\rho g}}$
However, this formula is valid only when the capillary tube is stationary on a surface and not falling or rising with respect to gravitational acceleration. When the tube is rising or falling, the gravitational acceleration will be replaced with the net acceleration of the object in the direction of gravity $(a)$ i.e.
 $\Rightarrow h={\displaystyle \frac{2T\cos \theta }{r\rho a}}$
Since the tube is free-falling in the scenario given to us, the net acceleration of the tube will $\Rightarrow a=g-g=0$
Then the height of rising inside the tube will be
 $\Rightarrow h={\displaystyle \frac{2T\cos \theta }{r\rho 0}}=\mathrm{\infty }$
Since the water can rise only up to the top of the capillary tube, the rise of water inside the tube will be 20 cm which corresponds to option (D).

Note
The water can only rise to the top of the capillary as surface tension will form a meniscus at the top of the capillary and won’t allow water to overflow outside the capillary. Whenever the tube is falling, we can expect the height of the water inside the capillary to increase since it will experience less gravitational acceleration so we can rule out options (A) and (C). The rise of water of 8 cm when the tube is stationary is also irrelevant since, in free fall, the water will rise to the height of the tube.