Answer :
Final answer:
The radius of the capillary tube resulting in water rising to a height of 10 cm, in relation to the original 5 cm rise in a 2 mm radius tube, is calculated to be 1 mm. So, the correct option is B.
Explanation:
The student is asking about the relationship between the height of water rise and the radius of a capillary tube due to capillary action. In physics, especially in the study of fluid dynamics, this phenomenon is explained by the Jurin's Law which describes the capillary rise phenomenon inversely proportional to the radius of the tube. The question specifies that water rises to a height of 5 cm in a capillary tube with a radius of 2 mm and seeks to find a new radius for a water rise of 10 cm.
To solve this, we apply the inverse proportionality relationship, where the height of water rise (h) is inversely proportional to the radius (r) of the tube. If we have two heights and corresponding radii (h1, r1) and (h2, r2), then h1/h2 = r2/r1. Plugging in the values from the question, we get 5 cm / 10 cm = (r2/2 mm), which simplifies to r2 = (5 cm / 10 cm) × 2 mm = 1 mm. Thus, the radius of the capillary tube in which water rises to a height of 10 cm is 1 mm, which corresponds to option B.
