Fluid Mechanics

JEE Main level, numerical answer, medium

134 of 192

Question 134 of 192

When a long glass capillary tube of radius 0.015cm0.015cm is dipped in a liquid, the liquid rises to a height of 15cm15cm within it. If the contact angle between the liquid and glass to close to 0∘0^{\circ}, the surface tension of the liquid, in milliNewton m−1,{m}^{-1}, is [ρ(liqued)=900kgm−3,g=10ms−2]\left[{\rho }_{\text{(liqued)}}=900kg{m}^{-3},g=10m{s}^{-2}\right] (Given answer in closed integer)

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Answer: 101

Using the concept of rise due to surface tension,
2Tr=hρg\dfrac{2T}{r}=h\rho g
T=rhρg2=15×10−5×15×10−2×900×102=101milliNewtonm−1T=\dfrac{rh\rho g}{2}=\dfrac{15\times {10}^{-5}\times 15\times {10}^{-2}\times 900\times 10}{2}=101milliNewton{m}^{-1}

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