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Answer :
Final answer:
In the physics concept of capillary action, the height water rises in a capillary tube is inversely proportional to the radius of the tube. When the water height rise is doubled, the tube's radius is halved. Therefore, the radius for the 10 cm height rise in water is 1 mm.
Explanation:
The subject of this question is the Physics of capillary action, specifically how the height to which water rises in a capillary tube relates to the radius of the tube. The capillary rise is inversely proportional to the radius of the capillary tube, which can be understood by considering the capillary action equation that includes surface tension, density of the liquid, acceleration due to gravity, the height the liquid rises, and the radius of the capillary tube.
In the given scenario, water rises up to a height of 5 cm in a capillary tube of radius 2 mm. If another capillary tube has water rising up to a height of 10 cm, we can say that the height to which the water rises is inversely proportional to the radius of the capillary tube. Therefore, if the height is doubled from 5 cm to 10 cm, the radius must be halved for it to rise twice as high. Hence, the radius of the tube in which the water rises to a height of 10 cm is 1 mm (option b).
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