A glass rod of radius r1 is inserted symmetrically into a vertical capillary tube of radius r2 such that their lower ends are at the same level. The arrangement is now dippedin water. The height to which water will rise into the tube will be (σ - surface tension of water ρ - density of water)
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a
σr2−r1ρg
b
2σr2−r1ρg
c
2σr2+r1ρg
d
2σr22+r12ρg
answer is B.
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Detailed Solution
Total upward force due to surface tension =σ2πr1+2πr2. This supports the weight of the liquid column of height h. Weight of liquid column =hπr22−πr12ρg Equating, we get hπr2+r1r2−r1ρg=2πσr1+r2⇒ hr2−r1ρg=2σ ⇒h=2σr2−r1ρg