The radii of the two columns in a U tube are | vedclass

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(A) The capillary rise in a tube of radius $r$ is given by the formula: $h = \frac{2T \cos 	heta}{ho rg}$.For the first arm with radius $r_1$,the c

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$\frac{\rho gh r_1 r_2}{2(r_2 - r_1)}$

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(A) The capillary rise in a tube of radius $r$ is given by the formula: $h = \frac{2T \cos 	heta}{ho rg}$.For the first arm with radius $r_1$,the capillary rise is $h_1 = \frac{2T \cos 0^o}{ho r_1 g} = \frac{2T}{ho r_1 g}$.For the second arm with radius $r_2$,the capillary rise is $h_2 = \frac{2T \cos 0^o}{ho r_2 g} = \frac{2T}{ho r_2 g}$.The level difference between the two arms is $h = h_1 - h_2$.Substituting the expressions for $h_1$ and $h_2$: $h = \frac{2T}{ho g} \left( \frac{1}{r_1} - \frac{1}{r_2} ight)$.Simplifying the term in the bracket: $h = \frac{2T}{ho g} \left( \frac{r_2 - r_1}{r_1 r_2} ight)$.Solving for surface tension $T$: $T = \frac{h ho g r_1 r_2}{2(r_2 - r_1)}$.

The radii of the two columns in a $U$ tube are $r_1$ and $r_2$. When a liquid of density $\rho$ (angle of contact is $0^o$) is filled in it,the level difference of liquid in the two arms is $h$. The surface tension of the liquid is ($g =$ acceleration due to gravity):

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