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80. Problem 17.56 (RHK) A solid glass rod of radius r= 1.3 cm is placed inside and coaxial with a glass cylinder of internal radius R=1.7 cm. Their bottom ends are aligned and placed in contact with, and perpendicular to, the surface of an open tank of water. We have to find the height y up to which the water will rise in the region between the rod and the cylinder. We can assume that the angle of contact is 00 and use 72.8 mN/m for the surface tension of water.
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Solution: Click For PDF Version Problem is a modification of the standard capillary rise in a tube due to surface tension. Total upward force on the liquid column contained between the coaxial glass rod and the cylinder is
where R is the radius of the cylinder, r is the radius of the
glass rod and
Weight of the liquid column supported by F is
Equating F and Mg,
Water will rise by 3.7 mm in the region between the rod and the cylinder.
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is the
surface tension of water.
