(D) The height $h$ to which a liquid rises in a capillary tube is given by the formula: $h = \frac{2T \cos \theta}{r \rho g}$.Since $T$,$\theta$,$\rho

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(D) The height $h$ to which a liquid rises in a capillary tube is given by the formula: $h = \frac{2T \cos \theta}{r \rho g}$.Since $T$,$\theta$,$\rho$,and $g$ are constants for the given liquid and tube material,we have the relation $h \propto \frac{1}{r}$,which implies $h_{1} r_{1} = h_{2} r_{2}$.Given $h_{1} = h$,$r_{1} = r$,and $r_{2} = \frac{r}{3}$.Substituting these values into the equation: $h \cdot r = h_{2} \cdot \frac{r}{3}$.Solving for $h_{2}$: $h_{2} = 3h$.

Class 11 Physics Fluid Mechanics and Surface Tension Capillary Tube and Capillarity

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When a capillary tube is immersed in water vertically,water rises to a height $h$ inside the tube. If the radius of another capillary tube is $\frac{1}{3}$ that of the previous,the height to which water will rise in this tube is:

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A
$h$
B
$h \sqrt{3}$
C
$\frac{h}{3}$
D
$3h$

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Fluid Mechanics and Surface Tension

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Capillary Tube and Capillarity

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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:

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Water rises in a capillary tube up to a height $h$. If this capillary tube is tilted by an angle of $45^o$,then the length of the water column in the capillary tube becomes

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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:

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When a capillary tube is immersed in water vertically,water rises to a height $h$ inside the tube. If the radius of another capillary tube is $\frac{1}{3}$ that of the previous,the height to which water will rise in this tube is:

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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:

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