Q 11-09-120JEE MainJEE Main 2021 (26 Aug, Shift 1)Medium
Two narrow bores of diameter $5.0$ mm and $8.0$ mm are joined together to form a $U$-shaped tube open at both ends. If this $U$-tube contains water, what is the difference in the level of two limbs of the tube. [Take surface tension of water $T = 7.3\times10^{-2}$ N m$^{-1}$, angle of contact $= 0$, $g = 10$ m s$^{-2}$ and density of water $= 1.0\times10^3$ kg m$^{-3}$]
Answer: (C) $2.19$ mm
Radii: $r_1 = 2.5$ mm, $r_2 = 4.0$ mm. The difference in capillary rise is
$$\Delta h = \frac{2T}{\rho g}\left(\frac{1}{r_1} - \frac{1}{r_2}\right) = \frac{2\times7.3\times10^{-2}}{10^3\times10}(400 - 250) = 2.19\times10^{-3}\ \text{m}$$
$\Delta h = 2.19$ mm.
Solution by Sreeraj P, M.Sc Physics