water rises to a height of 8cm in a capillary tube of length 20cm placed in a stationary lift. to what height would water rise if the lift is freely falling

To understand how water behaves in a capillary tube when the lift is freely falling, we need to consider the principles of capillarity and the effects of gravity. In a stationary lift, water rises to a height of 8 cm due to the balance between cohesive forces (the attraction between water molecules) and adhesive forces (the attraction between water molecules and the walls of the tube). When the lift is in free fall, however, the situation changes significantly.

Capillarity in a Stationary Lift

In a stationary lift, the water rises in the capillary tube due to the balance of forces. The height to which the water rises can be determined by the formula:

• h = (2 * γ * cos(θ)) / (ρ * g * r)

Where:

• h = height of the liquid column
• γ = surface tension of the liquid
• θ = contact angle
• ρ = density of the liquid
• g = acceleration due to gravity
• r = radius of the capillary tube

In this case, the water rises to 8 cm because the gravitational force is acting downwards, and the surface tension and adhesive forces are sufficient to overcome this force up to that height.

The Effect of Free Fall

When the lift is freely falling, the situation changes dramatically. In free fall, both the water and the lift experience the same acceleration due to gravity, effectively creating a condition of weightlessness. This means that the gravitational force acting on the water column is no longer countered by the adhesive and cohesive forces in the same way.

What Happens in Free Fall?

In a freely falling lift, the effective gravitational force acting on the water is zero. As a result, the water will not rise in the capillary tube at all. The adhesive forces that typically pull the water up the tube are now unopposed by gravity, leading to a situation where:

• The water does not rise above the bottom of the tube.

Thus, in a freely falling lift, the height to which water would rise in the capillary tube is effectively 0 cm.

Summary of the Concepts

To summarize, in a stationary lift, water rises to a height of 8 cm due to the balance of cohesive and adhesive forces against gravity. However, in a freely falling lift, the absence of effective gravitational force means that water will not rise at all, resulting in a height of 0 cm in the capillary tube. This illustrates the fascinating interplay between gravity and fluid dynamics in different conditions.