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Answer :
Final answer:
The mass of water that rises in a capillary tube of radius 2r compared to a tube of radius r is found to be double the mass, hence the answer is 2M. This conclusion is drawn based on the inverse proportionality of the water's height to the tube's radius and the quadratic increase in the tube's cross-sectional area. Therefore, the correct answer is A) 2M.
Explanation:
The question pertains to the concept of capillary action within the domain of physics, specifically relating to the mass of water that rises in capillary tubes with different radii.
According to the given equation, 2T cos 0 h = rpg, where h is the height of liquid inside the capillary tube, T is the surface tension, r is the radius of the tube, p is the density of the liquid, and g is the acceleration due to gravity. The equation implies that the height to which the water rises is inversely proportional to the radius of the tube.
Given this relationship, double the radius (2r) would result in the water rising to half the height that it would in a tube of radius r.
However, because the volume (and thus mass) of water is directly proportional to both the height to which it rises and the cross-sectional area of the tube (which quadruples when the radius is doubled, as the area is proportional to r2), the mass of water that will rise in a capillary tube of radius 2r would be 2M. Therefore, the correct answer is A) 2M.
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