Genius Physics (Class 11) - For IIT-JEE and CBSE

Pradeep Kshetrapal

Chapter 10

Surface Tension - all with Video Answers

Educators

Chapter Questions

Problem 1

A wooden stick $2 m$ long is floating on the surface of water. The surface tension of water $0.07 \mathrm{~N} / \mathrm{m}$. By putting soap solution on one side of the sticks the surface tension is reduced to $0.06 \mathrm{~N} / \mathrm{m}$. The net force on the stick will be
(a) $0.07 N$
(b) $0.06 \mathrm{~N}$
(c) $0.01 N$
(d) $0.02 N$

Saman Zulfiqar

Saman Zulfiqar

Numerade Educator

Problem 2

A wooden stick $2 m$ long is floating on the surface of water. The surface tension of water $0.07 \mathrm{~N} / \mathrm{m}$. By putting soap solution on one side of the sticks the surface tension is reduced to $0.06 \mathrm{~N} / \mathrm{m}$. The net force on the stick will be
(a) $0.07 N$
(b) $0.06 \mathrm{~N}$
(c) $0.01 N$
(d) $0.02 N$

Saman Zulfiqar

Numerade Educator

Problem 3

A $10 \mathrm{~cm}$ long wire is placed horizontally on the surface of water and is gently pulled up with a force of $2 \times 10^{-2} N$ to keep the wire in equilibrium. The surface tension in $\mathrm{Nm}^{-1}$ of water is
(a) $0.1 \mathrm{~N} / \mathrm{m}$
(b) $0.2 \mathrm{~N} / \mathrm{m}$
(c) $0.001 \mathrm{~N} / \mathrm{m}$
(d) $0.002 \mathrm{~N} / \mathrm{m}$

Saman Zulfiqar

Numerade Educator

Problem 4

There is a horizontal film of soap solution. On it a thread is placed in the form of a loop. The film is pierced inside the loop and the thread becomes a circular loop of radius $R$. If the surface tension of the loop be $T$, then what will be the tension in the thread
(a) $\pi R^{2} / T$
(b) $\pi R^{2} T$
(c) $2 \pi R T$
(d) $2 R T$

Saman Zulfiqar

Numerade Educator

Problem 5

A liquid is filled into a tube with semi-elliptical cross-section as shown in the figure. The ratio of the surface tension forces on the curved part and the plane part of the tube in vertical position will be
(a) $\frac{\pi(a+b)}{4 b}$
(b) $\frac{2 \pi a}{b}$
(c) $\frac{\pi a}{4 b}$
(d) $\frac{\pi(a-b)}{4 b}$

Saman Zulfiqar

Numerade Educator

Problem 6

A liquid film is formed over a frame $A B C D$ as shown in figure. Wire $C D$ can slide without friction. The mass to be hung from $C D$ to keep it in equilibrium is
(a) $\frac{T l}{g}$
(b) $\frac{2 T l}{g}$
(c) $\frac{g}{2 T l}$
(d) $T \times l$

Saman Zulfiqar

Numerade Educator

Problem 7

Two small drops of mercury, each of radius $R$, coalesce to form a single large drop. The ratio of the total surface energies before and after the change is
(a) $1: 2^{1 / 3}$
(b) $2^{1 / 3}: 1$
(c) $2: 1$
(d) $1: 2$

Saman Zulfiqar

Numerade Educator

Problem 8

Radius of a soap bubble is increased from $R$ to $2 R$ work done in this process in terms of surface tension is
[CPMT 1991; RPET 2001; BHU 2003]
(a) $24 \pi R^{2} S$
(b) $48 \pi R^{2} S$
(c) $12 \pi R^{2} S$
(d) $36 \pi R^{2} S$

Saman Zulfiqar

Numerade Educator

Problem 9

The work done in blowing a soap bubble of $10 \mathrm{~cm}$ radius is (surface tension of the soap solution is $\left.\frac{3}{100} N / m\right)$
[MP PMT 1995; MH CET 2002]
(a) $75.36 \times 10^{-4} J$
(b) $37.68 \times 10^{-4} J$
(c) $150.72 \times 10^{-4} J$
(d) $75.36 J$

Saman Zulfiqar

Numerade Educator

Problem 10

The work done in blowing a soap bubble of $10 \mathrm{~cm}$ radius is (surface tension of the soap solution is $\left.\frac{3}{100} N / m\right)$
[MP PMT 1995; MH CET 2002]
(a) $75.36 \times 10^{-4} J$
(b) $37.68 \times 10^{-4} J$
(c) $150.72 \times 10^{-4} J$
(d) $75.36 J$

Saman Zulfiqar

Numerade Educator

Problem 11

A drop of mercury of radius $2 \mathrm{~mm}$ is split into 8 identical droplets. Find the increase in surface energy. (Surface tension of mercury is $0.465 \mathrm{~J} / \mathrm{m}^{2}$ )
(a) $23.4 \mu J$
(b) $18.5 \mu \mathrm{J}$
(c) $26.8 \mu \mathrm{J}$
(d) $16.8 \mu J$

Saman Zulfiqar

Numerade Educator

Problem 12

The work done in increasing the size of a soap film from $10 \mathrm{~cm} \times 6 \mathrm{~cm}$ to $10 \mathrm{~cm} \times 11 \mathrm{~cm}$ is $3 \times 10^{-4} J$. The surface tension of the film is $\quad$ [MP PET 1999; MP PMT 2000; AIIMS 2000; JIPMER 2001, 02]
(a) $1.5 \times 10^{-2} \mathrm{Nm}^{-1}$
(b) $3.0 \times 10^{-2} \mathrm{Nm}^{-1}$
(c) $6.0 \times 10^{-2} \mathrm{Nm}^{-1}$
(d) $11.0 \times 10^{-2} \mathrm{Nm}^{-1}$

Saman Zulfiqar

Numerade Educator

Problem 13

If the work done in blowing a bubble of volume $V$ is $W$, then the work done in blowing the bubble of volume $2 V$ from the same soap solution will be
(a) $W / 2$
(b) $\sqrt{2} W$
(c) $\sqrt[3]{2} W$
(d) $\sqrt[3]{4} W$

Saman Zulfiqar

Numerade Educator

Problem 14

Several spherical drops of a liquid of radius $r$ coalesce to form a single drop of radius $R .$ If $T$ is surface tension and $V$ is volume under consideration, then the release of energy is
(a) $3 V T\left(\frac{1}{r}+\frac{1}{R}\right)$
(b) $3 V T\left(\frac{1}{r}-\frac{1}{R}\right)$
(c) $V T\left(\frac{1}{r}-\frac{1}{R}\right)$
(d) $V T\left(\frac{1}{r^{2}}+\frac{1}{R^{2}}\right)$

Saman Zulfiqar

Numerade Educator

Problem 15

The pressure inside a small air bubble of radius $0.1 \mathrm{~mm}$ situated just below the surface of water will be equal to (Take surface tension of water $70 \times 10^{-3} \mathrm{Nm}^{-1}$ and atmospheric pressure $=1.013 \times 10^{5} \mathrm{Nm}^{-2}$ ) [AMU (Med.) 2002]
(a) $2.054 \times 10^{3} \mathrm{~Pa}$
(b) $1.027 \times 10^{3} \mathrm{~Pa}$
(c) $1.027 \times 10^{5} \mathrm{~Pa}$
(d) $2.054 \times 10^{5} \mathrm{~Pa}$

Saman Zulfiqar

Numerade Educator

Problem 16

If the radius of a soap bubble is four times that of another, then the ratio of their excess pressures will be [AIIMS 2000]
(a) $1: 4$
(b) $4: 1$
(c) $16: 1$
(d) $1: 16$

Saman Zulfiqar

Numerade Educator

Problem 17

Pressure inside two soap bubbles are $1.01$ and $1.02$ atmospheres. Ratio between their volumes is
[MP PMT 1991]
(a) $102: 101$
(b) $(102)^{3}:(101)^{3}$
(c) $8: 1$
(d) $2: 1$

Saman Zulfiqar

Numerade Educator

Problem 18

The excess pressure inside an air bubble of radius $r$ just below the surface of water is $P_{1}$. The excess pressure inside a drop of the same radius just outside the surface is $P_{2}$. If $T$ is surface tension then
(a) $P_{1}=2 P_{2}$
(b) $P_{1}=P_{2}$
(c) $P_{2}=2 P_{1}$
(d) $P_{2}=0, P_{1} \neq 0$

Saman Zulfiqar

Numerade Educator

Problem 19

Water rises to a height of ocm in a capillary tube and mercury falls to a depth of $3.5 \mathrm{~cm}$ in the same capillary tube. If the density of mercury is $13.6 \mathrm{gm} / \mathrm{cc}$ and its angle of contact is $135^{\circ}$ and density of water is $1 \mathrm{gm} / \mathrm{cc}$ and its angle of contact is $0^{\circ}$, then the ratio of surface tensions of the two liquids is $\left(\cos 135^{\circ}=0.7\right)$
[MP PMT 1988; EAMCET (Med.) 2003]
(a) $1: 14$
(b) $5: 34$
(c) $1: 5$
(d) $5: 27$

Saman Zulfiqar

Numerade Educator

Problem 20

Water rises in a vertical capillary tube upto a height of $2.0 \mathrm{~cm}$. If the tube is inclined at an angle of $60^{\circ}$ with the vertical, then upto what length the water will rise in the tube
(a) $2.0 \mathrm{~cm}$
(b) $4.0 \mathrm{~cm}$
(c) $\frac{4}{\sqrt{3}} \mathrm{~cm}$
(d) $2 \sqrt{2} \mathrm{~cm}$

Saman Zulfiqar

Numerade Educator

Problem 21

Two capillary tubes of same diameter are kept vertically one each in two liquids whose relative densities are $0.8$ and o. 6 and surface tensions are 60 and 50 dyne $/ \mathrm{cm}$ respectively. Ratio of heights of liquids in the two tubes $\frac{h_{1}}{h_{2}}$ is [MP PMT 2002]
(a) $\frac{10}{9}$
(b) $\frac{3}{10}$
(c) $\frac{10}{3}$
(d) $\frac{9}{10}$

Saman Zulfiqar

Numerade Educator

Problem 22

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, mass of water that will rise in the capillary tube will now be
(a) $M$
(b) $2 M$
(c) $M / 2$
(d) $4 M$

Saman Zulfiqar

Numerade Educator

Problem 23

Water rises to a height $h$ in a capillary at the surface of earth. On the surface of the moon the height of water column in the same capillary will be
(a) $6 h$
(b) $\frac{1}{6} h$
(c) $h$
(d) Zero

Saman Zulfiqar

Numerade Educator

Problem 24

Water rises to a height $h$ in a capillary at the surface of earth. On the surface of the moon the height of water column in the same capillary will be
(a) $6 h$
(b) $\frac{1}{6} h$
(c) $h$
(d) Zero

Saman Zulfiqar

Numerade Educator

Problem 25

If the surface tension of water is $0.06 \mathrm{~N} / \mathrm{m}$, then the capillary rise in a tube of diameter $1 \mathrm{~mm}$ is $\left(\theta=0^{\circ}\right)$
[AFMC 1998]
(a) $1.22 \mathrm{~cm}$
(b) $2.44 \mathrm{~cm}$
(c) $3.12 \mathrm{~cm}$
(d) $3.86 \mathrm{~cm}$

Saman Zulfiqar

Numerade Educator

Problem 26

Two capillaries made of same material but of different radii are dipped in a liquid. The rise of liquid in one capillary is $2.2 \mathrm{~cm}$ and that in the other is $6.6 \mathrm{~m}$. The ratio of their radii is
(a) $9: 1$
(b) $1: 9$
(c) $3: 1$
(d) $1: 3$

Saman Zulfiqar

Numerade Educator

Problem 27

The lower end of a capillary tube is at a depth of $12 \mathrm{~cm}$ and the water rises $3 \mathrm{~cm}$ in it. The mouth pressure required to blow an air bubble at the lower end will be $X \mathrm{~cm}$ of water column where $X$ is $\quad$ [CPMT 1989$]$
(a) 3
(b) 9
(c) 12
(d) 15

Saman Zulfiqar

Numerade Educator

Problem 28

The lower end of a capillary tube of radius $r$ is placed vertically in water. Then with the rise of water in the capillary, heat evolved is
(a) $+\frac{\pi^{2} r^{2} h^{2}}{J} d g$
(b) $+\frac{\pi r^{2} h^{2} d g}{2 J}$
(c) $-\frac{\pi r^{2} h^{2} d g}{2 J}$
(d) $-\frac{\pi r^{2} h^{2} d g}{J}$

Saman Zulfiqar

Numerade Educator

Problem 29

Water rises in a capillary tube to a certain height such that the upward force due to surface tension is balanced by $75 \times 10^{-4} N$ force due to the weight of the liquid. If the surface tension of water is $6 \times 10^{-2} \mathrm{~N} / \mathrm{m}$, the inner circumference of the capillary must be
(a) $1.25 \times 10^{-2} \mathrm{~m}$
(b) $0.50 \times 10^{-2} \mathrm{~m}$
(c) $6.5 \times 10^{-2} \mathrm{~m}$
(d) $12.5 \times 10^{-2} \mathrm{~m}$

Mahipal Kumawat

Mahipal Kumawat

Numerade Educator

Problem 30

The radii of two soap bubbles are $r_{1}$ and $r_{2}$. In isothermal conditions, two meet together in vacuum. Then the radius of the resultant bubble is given by $\quad$ [RPET 1999; MP PMT 2001; EAMCET 2003]
(a) $R=\left(r_{1}+r_{2}\right) / 2$
(b) $R=r_{1}\left(r_{1} r_{2}+r_{2}\right)$
(c) $R^{2}=r_{1}^{2}+r_{2}^{2}$
(d) $R=r_{1}+r_{2}$

Saman Zulfiqar

Numerade Educator

Problem 31

Two soap bubbles of radii $r_{1}$ and $r_{2}$ equal to $4 \mathrm{~cm}$ and $5 \mathrm{~cm}$ are touching each other over a common surface $S_{1} S_{2}$ (shown in figure). Its radius will be
(a) $4 \mathrm{~cm}$
(b) $20 \mathrm{~cm}$
(c) $5 \mathrm{~cm}$
(d) $4.5 \mathrm{~cm}$

Saman Zulfiqar

Numerade Educator

Problem 32

An air bubble in a water tank rises from the bottom to the top. Which of the following statements are true
[Roorkee 2000]
(a) Bubble rises upwards because pressure at the bottom is less than that at the top
(b) Bubble rises upwards because pressure at the bottom is greater than that at the top
(c) As the bubble rises, its size increases
(d) As the bubble rises, its size decreases

Saman Zulfiqar

Numerade Educator

Problem 33

The radii of two soap bubbles are $R_{1}$ and $R_{2}$ respectively. The ratio of masses of air in them will be
(a) $\frac{R_{1}^{3}}{R_{2}^{3}}$
(b) $\frac{R_{2}^{3}}{R_{1}^{3}}$
(c) $\left(\frac{P+\frac{4 T}{R_{1}}}{P+\frac{4 T}{R_{2}}}\right) \frac{R_{1}^{3}}{R_{2}^{3}}$
(d) $\left(\frac{P+\frac{4 T}{R_{2}}}{P+\frac{4 T}{R_{1}}}\right) \frac{R_{2}^{3}}{R_{1}^{3}}$

Saman Zulfiqar

Numerade Educator

Problem 34

On dipping one end of a capillary in liquid and inclining the capillary at an angles $30^{\circ}$ and $60^{\circ}$ with the vertical, the lengths of liquid columns in it are found to be $l_{1}$ and $l_{2}$ respectively. The ratio of $l_{1}$ and $l_{2}$ is
(a) $1: \sqrt{3}$
(b) $1: \sqrt{2}$
(c) $\sqrt{2}: 1$
(d) $\sqrt{3}: 1$

Saman Zulfiqar

Numerade Educator

Problem 35

A drop of water of volume $V$ is pressed between the two glass plates so as to spread to an area $A$. If $T$ is the surface tension, the normal force required to separate the glass plates is
(a) $\frac{T A^{2}}{V}$
(b) $\frac{2 T A^{2}}{V}$
(c) $\frac{4 T A^{2}}{V}$
(d) $\frac{T A^{2}}{2 V}$

Narayan Hari

Numerade Educator