Capillary Action

Q. A capillary tube of radius $r$ is immersed in water and water rises in it to a height $h$. The mass of water in the capillary tube is $5\text{g}$. Another capillary tube of radius $2r$ is immersed in water. The mass of water that will rise in this tube is:

1. $2.5\text{g}$
2. $5.0\text{g}$
3. $10\text{g}$
4. $20\text{g}$

Q. Two mutually perpendicular wire carry charge densities ${\lambda }_1$ and ${\lambda }_2$. The electric line of force makes angle $\alpha$ with second wire, then the ratio $\frac{{\lambda }_1}{{\lambda }_2}$ is equal to (in terms of angle $\alpha )$

1. ${\cot }^2\alpha$
2. ${\tan }^2\alpha$
3. ${\sin }^2\alpha$
4. ${\cos }^2\alpha$

Q. 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 $\mathrm{T\; and}$ rise to the same height in three identical capillaries. The angles of contact ${\theta }_1,{\theta }_2$ and ${\theta }_3$ obey

1. $\pi >{\theta }_1>{\theta }_2>{\theta }_3>\frac{\pi }{2}$
2. $\frac{\pi }{2}>{\theta }_1>{\theta }_2>{\theta }_3\ge 0$
3. $0\le {\theta }_1<{\theta }_2<{\theta }_3<\frac{\pi }{2}$
4. $\frac{\pi }{2}<{\theta }_1<{\theta }_2<{\theta }_3<\pi$

Q. If a capillary tube is dipped into liquid and the level of the liquid inside and outside are same, then the angle of contact is

1. $0^{\circ }$
2. ${90}^{\circ }$
3. ${45}^{\circ }$
4. ${30}^{\circ }$

Q. The end of a capillary tube with radius $r$ is immersed in water. Assuming the tube to be sufficiently long, calculate the heat energy produced when the water rises in the tube.
[Assume angle of contact = $0^{\circ }$ for glass-water system]
$\rho =$ density of water, $T=$ surface tension of water

1. $0$
2. $\frac{\pi T^2}{\rho g}$
3. $\frac{2\pi T^2}{\rho g}$
4. $\frac{4\pi T^2}{\rho g}$

Q. Two mutually perpendicular infinite wires along $\text{x-}$axis and $\text{y-}$axis carry charge density ${\lambda }_1$ and ${\lambda }_2$. The electric line of force at $\text{P}$ is along the line $y=\frac{x}{\sqrt{3}}$, where $\text{P}$ is also a point lying on the same line, then find $\frac{{\lambda }_1}{{\lambda }_2}$

1. $2$
2. $1$
3. $\frac{1}{2}$
4. $\frac{1}{3}$

Q. Water rises in a capillary tube upto a height of $50\text{cm}$. The length of the water column when the capillary tube is tilted at an angle of ${45}^{\circ }$ is

1. $\frac{50}{\sqrt{2}}\text{cm}$
2. $50\sqrt{2}\text{cm}$
3. zero
4. None of these

Q. A $20\text{cm}$ long capillary tube is dipped in water. The water rises upto $8\text{cm}$. If the entire arrangement is put in a freely falling elevator, the length of water column in the capillary tube will be

1. $8\text{cm}$
2. $10\text{cm}$
3. $4\text{cm}$
4. $20\text{cm}$

Q. If $M$ is the mass of water that rises in a capillary tube of radius $r$, then mass of water which will rise in a capillary tube (of same material) of radius $2r$ is

1. $2M$
2. $4M$
3. $M/2$
4. $M$

Q. Due to capillary action, a liquid will rise in a tube if the angle of contact is

1. Acute
2. Obtuse
3. ${90}^{\circ }$
4. ${180}^{\circ }$

Q. The shape of the meniscus for a liquid with angle of contact equal to ${90}^{\circ }$ is:

1. Flat
2. Parabolic
3. Hemispherical
4. Cylindrical

Q. The work done in increasing the size of a soap film from $10\text{cm}\times 6\text{cm}$ to $10\text{cm}\times 11\text{cm}$ is $3\times {10}^{–4}\text{J}$. The surface tension of the film is

1. $3.0\times {10}^{-2}\text{N/m}$
2. $6.0\times {10}^{-2}\text{N/m}$
3. $1.5\times {10}^{-2}\text{N/m}$
4. $11.0\times {10}^{-2}\text{N/m}$

Q. A glass capillary tube of inner diameter $0.28\text{mm}$ is lowered vertically into water in a vessel. The pressure to be applied on the water in the capillary tube so that water level in the tube is same as that in the vessel $\left({\text{in N/m}}^2\right)$ is
(Surface tension of water $=0.07\text{N/m}$ and atmospheric pressure $={10}^5{\text{N/m}}^2)$

1. ${10}^3$
2. $99\times {10}^3$
3. $100\times {10}^3$
4. $101\times {10}^3$

Q. Two parallel glass plates are dipped partly in a liquid of density ${}^{\prime }{d}^{\prime }$ keeping them vertical. If the distance between the plates is ${}^{\prime }{x}^{\prime }$, surface tension for the liquid is $T$ and angle of contact is $\theta$, then rise of liquid between the plates due to capillary action will be:

1. $\frac{T\cos \theta }{xd}$
2. $\frac{T\cos \theta }{xdg}$
3. $\frac{2T\cos \theta }{xdg}$
4. $\frac{2T}{xdg\cos \theta }$

Q. Water rises in a capillary tube to a certain height such that the upward force due to surface tension is balanced by $75\times {10}^{-4}\text{N}$ force due to the weight of the liquid. If the surface tension of water is $6\times {10}^{-2}\text{N/m}$, the inner circumference of the capillary tube must be: (Take $\theta =0^{\circ })$

1. $6.5\times {10}^{-2}\text{m}$
2. $12.5\times {10}^{-2}\text{m}$
3. $1.25\times {10}^{-2}\text{m}$
4. $0.50\times {10}^{-2}\text{m}$

Q. A vertical glass capillary tube, open at both ends, contains some water. Which of the following shapes can not be taken by the water in the tube?

1. 
2. 
3. 
4. 

Q. A steel rod of cross-sectional area $1{\text{m}}^2$ is acted upon by forces as shown in the figure. The total elongation of the bar is (Take $Y=2.0\times {10}^{11}{\text{Nm}}^{-2}$)

1. $11\times {10}^{-7}\text{m}$
2. $13\times {10}^{-7}\text{m}$
3. $15\times {10}^{-7}\text{m}$
4. $17\times {10}^{-7}\text{m}$

Q.

Due to capillary action, a liquid will rise in a tube, if the angle of contact is

1. Acute

2. Obtuse

3. 90°

4. Zero

Q. A liquid of density $\rho$ and surface tension $\sigma$ rises to a height $h$ in a capillary tube of diameter $d$. The potential energy of the liquid in the capillary tube is:
[Assume liquid to be perfectly wetting in nature]

1. $h\rho g$
2. $\frac{2\pi {\sigma }^2}{\rho g}$
3. $2\pi {\sigma }^2\rho g$
4. $\frac{2\pi {\sigma }^2}{\rho gh}$

Q.

A steel wire of original length 1 m and cross-sectional area $4.00m{m}^2$ is clamped at the two ends so that it lies horizontally and without tension. If a load of 2.16 kg is suspended from the middle point of the wire, what would be its vertical depression ?

Y of the steel = $2.0\times {10}^{11}N{m}^{-2}.Takeg=10m{s}^{-2}$.

Q.

The liquid meniscus in capillary tube will be convex, if the angle of contact is

1. Greater than 90⁰

2. Less than 90°

3. Equal to 90°

4. Equal to 0°

Q. If the capillarity rise in two tubes containing same liquid and made of same material are $6.6\text{cm}$ and $2.2\text{cm}$, then the ratio of the radii of the tubes is

1. $1:3$
2. $3:1$
3. $1:6$
4. $1:2$

Q. A capillary tube $A$ is dipped in water. Another identical capillary tube $B$ is dipped in soap- water solution. Which of the following shows the relative nature of the liquid columns in the two tubes? Consider the surface tension of soap solution and water to be $0.073\text{N/m}$ and $0.025\text{N/m}$ respectively at room temperature.

1. 
2. 
3. 
4. 

Q.

Water rises to height $h$ in the capillary tube. If the length of the capillary tube above the surface of the water is made less than $h$ then:

1. Water does not rise at all.

2. Water rises up to a point a little below the top and stays there.

3. Water rises up to the tip of the capillary tube and then starts overflowing like a fountain.

4. Water rises up to the top of the capillary tube and stays there without overflowing.

Q. When a tube of length $10\text{cm}$ is dipped in water, the water rises up to $6\text{cm}$. If the entire arrangement is put in a freely falling elevator, the length of water column in the capillary tube will be

1. $2\text{cm}$
2. $6\text{cm}$
3. $10\text{cm}$
4. $4\text{cm}$

Q.

How is the capillary effect related to the contact angle?

Q. A capillary tube of radius $r$ is immersed vertically in a liquid such that the liquid rises in it to height $h$ (less than the length of the tube). Mass of the liquid in the capillary tube is $m$. If the radius of the capillary tube is increased by $50\%$, then the mass of the liquid that will rise in the tube is:

1. $\frac{2}{3}m$
2. $m$
3. $\frac{3}{2}m$
   
4. $\frac{9}{4}m$
   

Q. A liquid does not wet the surface of a solid, if the angle of contact is

1. Zero
2. Acute (less than ${90}^{\circ })$
3. Obtuse (more than ${90}^{\circ })$
4. ${90}^{\circ }\left(\text{right angle}\right)$

Q. A capillary tube of radius $R$ is immersed in water and water rises in it to a height $H$. Mass of water in the capillary tube is $M$. If the radius of the tube is doubled, then the mass of water that rises in the capillary tube will be:

1. $M$
2. $2M$
3. $\frac{M}{2}$
4. $4M$

Q. Water rises in a vertical capillary tube up to $2\sqrt{2}\text{cm}$. If the tube is inclined at an angle ${\theta }^{\circ }$, the length of water risen in the tube is $4\text{cm}$. Find the value of $\theta$.

1. ${30}^{\circ }$
2. ${37}^{\circ }$
3. ${60}^{\circ }$
4. ${45}^{\circ }$