(C) The effective radius of the annular space between the glass rod and the capillary tube is given by the difference in their radii: $r_{eff} = r_2 -

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(C) The effective radius of the annular space between the glass rod and the capillary tube is given by the difference in their radii: $r_{eff} = r_2 - r_1 = 2.0\,mm - 1.0\,mm = 1.0\,mm = 1.0 \times 10^{-3}\,m$.Using the formula for capillary rise in an annular space: $h = \frac{2T}{\rho g r_{eff}}$.Substituting the given values: $T = 75 \times 10^{-3}\,N/m$,$\rho = 10^3\,kg/m^3$,$g = 10\,m/s^2$,and $r_{eff} = 1.0 \times 10^{-3}\,m$.$h = \frac{2 \times 75 \times 10^{-3}}{10^3 \times 10 \times 1.0 \times 10^{-3}} = \frac{150 \times 10^{-3}}{10} = 15 \times 10^{-3}\,m$.Converting to millimeters: $h = 15\,mm$.

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

Medium

$A$ glass rod of radius $1.0\,mm$ is inserted symmetrically into a vertical capillary tube of radius $2.0\,mm$ such that their lower ends are at the same level. This arrangement is now dipped in water. The height to which water will rise into the tube will be ...... $mm$ (Surface Tension of water $T = 75 \times 10^{-3}\,N/m$,density $\rho = 10^3\,kg/m^3$,$g = 10\,m/s^2$).

A
$5$
B
$10$
C
$15$
D
$20$

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Class 11 Questions

Class 11

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Fluid Mechanics and Surface Tension

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Capillary Tube and Capillarity

Water rises to a height $h$ in a capillary tube at the surface of the Earth. On the surface of the moon,the height of the water column in the same capillary tube will be:

Medium

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$A$ capillary tube is taken from the Earth's surface to the Moon's surface. What happens to the rise of the liquid column on the Moon's surface? (Acceleration due to gravity on the Earth's surface is six times that of the Moon's surface.)

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When a capillary tube is dipped vertically in water,the water rises to a height of $2.0 \, cm$. If the capillary tube is tilted at an angle of $60^\circ$ with the vertical,what will be the length of the water column in the capillary tube in $cm$?

Medium

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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:

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$A$ capillary tube is dipped in water and it is $20 \, cm$ outside water. The water rises up to $8 \, cm$. If the entire arrangement is put in a freely falling elevator,the length of the water column in the capillary tube will be ........ $cm$.

Easy

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Water rises to a height $h$ in a capillary tube at the surface of the Earth. On the surface of the moon,the height of the water column in the same capillary tube will be:

$A$ capillary tube is taken from the Earth's surface to the Moon's surface. What happens to the rise of the liquid column on the Moon's surface? (Acceleration due to gravity on the Earth's surface is six times that of the Moon's surface.)

When a capillary tube is dipped vertically in water,the water rises to a height of $2.0 \, cm$. If the capillary tube is tilted at an angle of $60^\circ$ with the vertical,what will be the length of the water column in the capillary tube in $cm$?

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:

$A$ capillary tube is dipped in water and it is $20 \, cm$ outside water. The water rises up to $8 \, cm$. If the entire arrangement is put in a freely falling elevator,the length of the water column in the capillary tube will be ........ $cm$.

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