Answer :
Water will rise nine times higher in the second capillary tube with a radius one third of the first, resulting in a height of 18.0 cm due to capillary action, as height is inversely proportional to the radius squared.
The phenomenon in question is known as capillary action, which is a principle in physics involving the movement of liquids within narrow spaces without the assistance of, and often in opposition to, external forces like gravity. This is observed when water rises in capillary tubes. According to the Jurin's law, the height to which a liquid can rise or fall in a capillary tube is inversely proportional to the radius of the tube. The formula for capillary rise is h = (2T)/(rpg), where h is the height the liquid rises, T is the liquid's surface tension, r is the radius of the tube, p is the density of the liquid, and g is the acceleration due to gravity.
Given that water rises to a height of 2.0 cm in one capillary tube, in a second tube with a radius one third of the first, water would rise to a height nine times that, because the capillary rise is inversely proportional to the radius squared (hence the factor of 3 squared, or 9). This results in the water rising to a height of 18.0 cm in the second tube.
According to Jurin's Law, water will rise three times higher in the second capillary tube with a radius one third of the first, resulting in a height of 6.0 cm.
The question regards the phenomenon of capillary action, which refers to the ability of a liquid to flow in narrow spaces without the assistance of external forces. When dealing with capillary tubes, the height to which a liquid rises is inversely proportional to the radius of the tube, according to Jurin's Law. Specifically, the height to which the liquid rises is given by the equation \\(h \propto 1/r\\), where \\(h\\) is the height and \\(r\\) is the radius of the tube.
Given that water rises to a height of 2.0 cm in the first capillary tube, if the second tube has a radius that is one third of the first, according to Jurin's Law, the water in the second capillary tube will rise to a height that is three times that of the first. Therefore, the water will rise to a height of \\(2.0 \text{ cm} \times 3 = 6.0 \text{ cm}\\).
