A 20 cm long capillary tube is dipped in water. The water rises up to 8 cm. If the entire arra

step 1 We are given that the capillary tube Capillary tube height as equal to 20 centimeter 20 centimet

A 20 cm long capillary tube is dipped in water. The water...

A $20 \mathrm{~cm}$ long capillary tube is dipped in water. The water rises up to $8 \mathrm{~cm}$. If the entire arrangement is put in a freely falling elevator, the length of water column in the capillary tube will be (A) $8 \mathrm{~cm}$ (B) $10 \mathrm{~cm}$ (C) $4 \mathrm{~cm}$ (D) $20 \mathrm{~cm}$

A $20 \mathrm{~cm}$ long capillary tube is dipped in water. The water rises up to $8 \mathrm{~cm}$. If the entire arrangement is put in a freely falling elevator, the length of water column in the capillary tube will be
(A) $8 \mathrm{~cm}$
(B) $10 \mathrm{~cm}$
(C) $4 \mathrm{~cm}$
(D) $20 \mathrm{~cm}$

Key Concepts

Hydrostatic Pressure Balance

Hydrostatic pressure balance in the context of capillary rise involves the equilibrium between the upward capillary force (derived from surface tension and the properties of the liquid-solid interface) and the downward gravitational force acting on the liquid column. This balance determines the equilibrium height of the liquid column in a capillary tube. In situations where the effective gravitational acceleration is reduced, such as in free fall, this balance is disrupted, leading to a significantly different behavior of the liquid column.

Effective Gravity in Non-Inertial Frames

Effective gravity refers to the apparent gravitational force experienced in a non-inertial frame, such as a freely falling elevator. In such a frame, the acceleration due to gravity is effectively reduced or even nullified, which in turn affects phenomena like capillary rise. When effective gravity becomes zero, the hydrostatic pressure difference that normally opposes the capillary forces vanishes, altering the equilibrium configuration of the liquid column.

Surface Tension

Surface tension is the elastic tendency of a fluid surface which makes it acquire the least surface area possible. It arises from the cohesive forces among liquid molecules and is crucial in capillary phenomena because it generates the pressure difference across the curved liquid interface (meniscus) inside the capillary tube. This pressure difference enables the liquid to climb upward in the presence of adhesive interactions with the tube walls.

Capillary Action

Capillary action is the phenomenon by which a liquid can flow in narrow spaces without external forces, due to the interplay of adhesive forces between the liquid and the solid surface and cohesive forces within the liquid. This effect is what allows liquids to rise or fall in a thin tube relative to the surrounding level, and it is quantitatively described by Jurin’s Law, which relates the height of the liquid column to surface tension, the contact angle, the density of the liquid, and the effective gravitational acceleration.

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