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In a surface tension experiment with a capillary tube, water rises up to \[0.1m\] . If the same experiment is repeated in an artificial satellite revolving around the earth. Then the water will rise in the capillary up to a height of:
A) $0.1m$
B) \[9.8m\]
C) \[0.98m\]
D) Full length of capillary tube.

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Last updated date: 17th Jun 2024
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Answer
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Hint:The liquid rise in the capillary tube is directly proportional to surface tension of the liquid, inversely proportional to density and inversely proportional to radius of the tube and acceleration due to gravity.

Complete step by step answer:
Height of capillary rise of liquid is given by, $H = \dfrac{{2T}}{{\rho gr}}$
Where, $T$ is called surface tension of the liquid
$r$ is the radius of the capillary tube
$g$ is acceleration due to gravity.
$\rho $ is the density of the liquid.
On the surface of earth water rises up to $0.1m$. Now if the same experiment is repeated in an artificial satellite revolving around the earth then acceleration due to gravity is negligibly very small. Because there is a state of weightlessness, that is,$g = 0m{s^{ - 2}}$
Since acceleration due to gravity ‘$g$’ is in the denominator thus, the value of h becomes infinity. That is,$ \Rightarrow H = \dfrac{{2T}}{{0 \times gr}} = \infty $
That means, there will be no overflowing of water in the tube and water stands up to maximum height in the tube available. That is the full length of the capillary tube.

Thus, correct option is (D)

Additional information:
We know that rising of liquid in a capillary tube is stopped when surface tension force as well as weight of the liquid column balances. This condition is called equilibrium condition
Capillary tube is a tube with a fine pore. When a capillary tube of glass is dipped into water or any other liquid that wets the glass it is found that the liquid rises in the tube. When a capillary tube of glass is immersed in mercury or any other liquid that does not wet glass, the depression in the tube is produced.

The rise or fall of liquid in a capillary tube immersed partially in the liquid is called capillarity.

Note:
Applications of capillarity: due to capillarity
(1) water rises in plants from root to the top.
(2) blood flows in the veins of the body.
(3) a sponge retains water in it after dipping it once in water and
(4) kerosene flows from the bottom to the tip of the wick in the kerosene lamp.
Capillary is due to the property of surface tension.