(B) The pressure difference across the meniscus of the water in the capillary is given by the Young-Laplace equation: $\Delta P = 2T/R_{eff}$.Here, th

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(B) The pressure difference across the meniscus of the water in the capillary is given by the Young-Laplace equation: $\Delta P = 2T/R_{eff}$.Here, the effective radius of the capillary space is the gap between the tube and the wire, which is $R_{eff} = R - r$.At equilibrium, the pressure difference balances the hydrostatic pressure of the water column of height '$h$': $\Delta P = h\rho g$.Equating the two expressions: $2T/(R-r) = h\rho g$.Solving for '$h$': $h = 2T/((R-r)\rho g)$.

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

Difficult

In a capillary tube of radius '$R$',a straight thin metal wire of radius '$r$' is inserted symmetrically and one end of the combination is dipped vertically in water such that the lower end of the capillary and the thin wire are at the same level. If '$T$' is the surface tension of water and '$\rho$' is the density of water, then the rise of water in the capillary is:

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A
$T/((R-r)\rho g)$
B
$2T/((R-r)\rho g)$
C
$4T/((R+r)\rho g)$
D
$T/((R+r)\rho g)$

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Class 11 Questions

Class 11

Physics Questions

Chapter

Fluid Mechanics and Surface Tension

Subtopic

Capillary Tube and Capillarity

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$A$ capillary tube of radius $R$ is dipped in water,and water rises to a height $H$. The mass of water in the capillary tube is $M$. If a capillary tube of half the radius is dipped in water,what will be the mass of the water in the capillary tube?

Medium

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

Easy

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Two capillary tubes of same diameter are put vertically one each in two liquids whose relative densities are $0.8$ and $0.6$ and surface tensions are $60$ and $50 \text{ dyne/cm}$ respectively. The ratio of the heights of the liquids in the two tubes $\frac{h_1}{h_2}$ is:

Medium

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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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Water rises up to a height $h$ in a capillary tube immersed vertically in water. When this whole arrangement is taken to a depth $d$ in a mine,the water level rises up to a height $h^{\prime}$. If $R$ is the radius of the earth,then the ratio $\frac{h}{h^{\prime}}$ is

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$A$ capillary tube of radius $R$ is dipped in water,and water rises to a height $H$. The mass of water in the capillary tube is $M$. If a capillary tube of half the radius is dipped in water,what will be the mass of the water in the capillary tube?

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

Two capillary tubes of same diameter are put vertically one each in two liquids whose relative densities are $0.8$ and $0.6$ and surface tensions are $60$ and $50 \text{ dyne/cm}$ respectively. The ratio of the heights of the liquids in the two tubes $\frac{h_1}{h_2}$ is:

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):

Water rises up to a height $h$ in a capillary tube immersed vertically in water. When this whole arrangement is taken to a depth $d$ in a mine,the water level rises up to a height $h^{\prime}$. If $R$ is the radius of the earth,then the ratio $\frac{h}{h^{\prime}}$ is

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