Answer :
Final answer:
To calculate the radius for water to rise to 10 cm in a capillary tube, we use the principle of capillary action to find that the radius is 1 mm, making option B correct. The correct option is (b).
Explanation:
To determine the radius of the capillary tube for water to rise to a height of 10 cm, we use the concept of capillary action, which is governed by the capillary rise equation:
The height (h) of the liquid column is inversely proportional to the radius (r) of the capillary, given by the equation h = (2T)/(rho g), where T is the surface tension of the liquid, ρ is the density of the liquid, and g is the acceleration due to gravity. Assuming all conditions remain constant except for the radius of the tube, we can say that h1r1 = h2r2. Given h1 = 5 cm and r1 = 2 mm for the first capillary, and h2 = 10 cm, we can rearrange the equation to solve for r2, yielding:
r2 = (h1 * r1) / h2
Substituting in the values gives us:
r2 = (5 cm * 2 mm) / 10 cm
This simplifies to:
r2 = 1 mm
