A capillary tube of radius r is immersed vertically in a liquid such that liquid rises in it to height h (less than the length of the tube). Mass of liquid in the capillary tube is m . If radius of th

Question

A capillary tube of radius r is immersed vertically in a liquid such that liquid rises in it to height h (less than the length of the tube). Mass of liquid in the capillary tube is m . If radius of the capillary tube is increased by 50% , then mass of liquid that will rise in the tube, is

TestHub · Accepted Answer

h = r ρ g 2 T c o s θ ​ ⇒ h ∝ r 1 ​ ⇒ h 1 ​ h 2 ​ ​ = r 2 ​ r 1 ​ ​ = 3 2 ​ ( ∵ r 1 ​ = r , r 2 ​ New mass m 2 ​ = π r 2 2 ​ h 2 ​ ρ ​ = r + 50% of r = 2 3 ​ r ) = π ( 2 3 ​ r 1 ​ ) 2 ( 3 2 ​ h 1 ​ ) ρ = 2 3 ​ ( π r 1 2 ​ h 1 ​ ) ρ = 2 3 ​ m ​

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