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

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(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

Vedclass · Accepted Answer

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

Vedclass · Answer

(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):

Similar Questions

If a capillary experiment is performed in a vacuum,what happens to the liquid level in the capillary tube?

Three liquids of densities $\rho_1, \rho_2$ and $\rho_3$ (with $\rho_1 > \rho_2 > \rho_3$),having the same value of surface tension $T$,rise to the same height in three identical capillaries. The angles of contact $\theta_1, \theta_2$ and $\theta_3$ obey:

Water rises to a height of $16.3 \, cm$ in a capillary tube of height $18 \, cm$ above the water level. If the tube is cut at a height of $12 \, cm$ above the water level,then:

When a capillary tube is dipped into two liquids having relative densities $0.8$ and $0.6$ and surface tensions $60 \, dyne/cm$ and $50 \, dyne/cm$ respectively,the ratio of the heights of the liquids in the capillary tube $\frac{h_1}{h_2}$ is:

Vedclass Test Series

Exam Paper Generator

Online Exam Module