(B) The capillary rise $h$ is given by $h = \frac{2T \cos \theta}{r \rho g}$. When the tube is cut at a height $h' = 12 \,cm$,which is less than the n

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Water will stay at a height of $12 \,cm$ in the capillary tube.

(B) The capillary rise $h$ is given by $h = \frac{2T \cos \theta}{r \rho g}$. When the tube is cut at a height $h' = 12 \,cm$,which is less than the natural rise of $16.3 \,cm$,the water will not overflow. Instead,the radius of curvature $R$ of the meniscus will adjust itself such that $h' = \frac{2T \cos \theta'}{R \rho g} = 12 \,cm$. Thus,the water will simply rise to the top of the cut tube and stay there,forming a meniscus with a larger radius of curvature.

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

Easy

Water rises to a height of $16.3 \,cm$ in a capillary tube. If the tube is cut at a height of $12 \,cm$ above the water level,what will happen?

A
Water will come out as a fountain from the capillary tube.
B
Water will stay at a height of $12 \,cm$ in the capillary tube.
C
The height of the water in the capillary will be $10.3 \,cm$.
D
Water will flow down the sides of the capillary tube.

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Class 11

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Fluid Mechanics and Surface Tension

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Capillary Tube and Capillarity

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Water rises in a capillary tube to a height of $3\, cm$ when one end is dipped vertically in it. If the surface tension of water is $75 \times 10^{-3}\, N/m$,then the diameter of the capillary tube will be....... $mm$. (Assume $g = 10\, m/s^2$)

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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 ........ $cm$.

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Water rises to a height of $10$ cm in a capillary tube and mercury falls to a depth of $3.112$ cm in the same capillary tube. If the density of mercury is $13.6 \text{ g/cm}^3$ and the angle of contact for mercury is $135^o$,the ratio of surface tension of water and mercury is (Assume density of water = $1 \text{ g/cm}^3$ and angle of contact for water = $0^o$)

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Two narrow tubes of diameters $d_1$ and $d_2$ are joined together to form a $U$-tube open at both ends. If the $U$-tube contains water,the difference in water levels in the limbs is ($T$ is the surface tension of water,the angle of contact is zero,the density of water is $\rho$,and $g$ is the acceleration due to gravity).

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Water rises to a height of $16.3 \,cm$ in a capillary tube. If the tube is cut at a height of $12 \,cm$ above the water level,what will happen?

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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.)

Water rises in a capillary tube to a height of $3\, cm$ when one end is dipped vertically in it. If the surface tension of water is $75 \times 10^{-3}\, N/m$,then the diameter of the capillary tube will be....... $mm$. (Assume $g = 10\, m/s^2$)

$A$ 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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