#### Question

Water rises to a height 3.2 cm in a glass capillary tube. Find the height to which the same water will rise in another glass capillary having half area of cross section.

#### Solution

The surface tension of water placed in a capillary is given in terms of height of the water column, angle of contact between water and glass which is 0°, radius of the capillary tube, density of the water, and the acceleration due to gravity as follows,

T = hρgr/2cosθ

the question says that the radius of the tube is decreased to 1/2 of the original value. Therefore the surface tension becomes

T' = h'ρg(r/2)/2cosθ

on comparing both equations we get,

hρgr/2cosθ = h'ρg(r/2)/2cosθ

∴ hr = h'r/2

∴ h = h'/2

∴ h' = 2h

∴ h' = 2 × 3.2

∴ h' = 6.4cm

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#### APPEARS IN

Solution Find the Height to Which the Same Water Will Rise in Another Glass Capillary Having Half Area of Cross Section. Concept: Surface Tension.