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  4. When a long glass capillary tube of radius 0.015 cm is dipped in a liquid, the liquid rises to a height of 15 cm within it. If the contact angle between the liquid and glass to close to 0°, the surface tension of the liquid, in milliNewton m -1, is [ρ( text liquid )=900 kgm -3, g =10 ms -2] (Give answer in closest integer).

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Q. When a long glass capillary tube of radius $0.015 \,cm$ is dipped in a liquid, the liquid rises to a height of $15\, cm$ within it. If the contact angle between the liquid and glass to close to $0^{\circ},$ the surface tension of the liquid, in milliNewton $m ^{-1}$, is
$\left[\rho_{(\text {liquid })}=900 kgm ^{-3}, g =10 ms ^{-2}\right]$ (Give answer in closest integer)_________.

JEE MainJEE Main 2020Mechanical Properties of Fluids

Solution:

Capillary rise
$h =\frac{2 S \cos \theta}{\rho gr }$
$S =\frac{\rho grh }{2 \cos \theta}$
$=\frac{(900)(10)\left(15 \times 10^{-5}\right)\left(15 \times 10^{-2}\right)}{2}$
$S =1012.5 \times 10^{-4}$
$S =101.25 \times 10^{-3}=101.25 mN / m$
In question closest integer is asked
so closest integer $=101.00$ Ans.