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Answer :
Final answer:
The mass of water that rises in a capillary tube of radius '2r' is four times the mass that rises in a tube of radius 'r', so the correct answer is d. 4m.
Explanation:
The question involves the concept of capillary action, a topic within Physics. Specifically, it deals with the relationship between the capillary tube radius and the mass of water that will rise due to capillary action. The height to which water rises in a capillary tube is inversely proportional to the radius of the tube, according to the capillary rise formula h = (2T cos θ) / (rpg), where h represents the height, T is the surface tension, θ is the contact angle, r is the radius of the tube, p is the density of the liquid, and g is the acceleration due to gravity.
Given that the mass of water is directly proportional to the volume of water raised and taking into account that the volume is a function of the square of the radius, when the radius of the capillary tube is doubled (to '2r'), the cross-sectional area of the tube increases by a factor of four. Consequently, the mass of the water that will rise in a capillary tube of radius '2r' is four times the mass that would rise in a tube of radius 'r', assuming the same height of capillary rise.
Therefore, the correct answer to the question, 'If m is the mass of water that rises in a capillary tube of radius r, then the mass of water that will rise in a capillary tube of radius 2r is:', would be d. 4m.
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