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 $\times$ 10^$-$2 Nm^$-$1, angle of contact = 0, g = 10 ms² and density of water = 1.0 $\times$ 10³ kg m^$-$3]

Image<br><br>We have, P_A = P_B. [Points A &amp; B at same horizontal level]<br><br>$\therefore$ $${P_{atm}} - {{2T} \over {{r_1}}} + \rho g(x + \Delta h) = {P_{atm}} - {{2T} \over {{r_2}}} + \rho gx$$<br><br>$\therefore$ $\rho g\Delta h = 2T\left[ {{1 \over {{r_1}}} - {1 \over {{r_2}}}} \right]$<br><br>$$ = 2 \times 7.3 \times {10^{ - 2}}\left[ {{1 \over {2.5 \times {{10}^{ - 3}}}} - {1 \over {4 \times {{10}^{ - 3}}}}} \right]$$<br><br>$\therefore$ $$\Delta h = {{2 \times 7.3 \times {{10}^{ - 2}} \times {{10}^3}} \over {{{10}^3} \times 10}}\left[ {{1 \over {2.5}} - {1 \over 4}} \right]$$<br><br>= 2.19 $\times$ 10^$-$3 m = 2.19 mm<br><br>Hence, option (b).