Objective Physics for NEET

Abhay Kumar

Chapter 9

Elasticity and Surface Tension - all with Video Answers

Educators

Chapter Questions

Problem 1

A wire can be broken by applying a load of $20 \mathrm{~kg}$ wt. The force required to break the wire of twice the diameter is
(a) $20 \mathrm{~kg} \mathrm{wt}$
(b) $5 \mathrm{~kg} \mathrm{wt}$
(c) $80 \mathrm{~kg} \mathrm{wt}$
(d) $160 \mathrm{~kg}$ wt

Darmendar Jain

Darmendar Jain

Numerade Educator

Problem 2

If $B$ is the bulk modulus of a metal and a pressure $P$ is applied uniformly on all sides of the metal with density $D$, then the fractional increase in density is given by
(a) $\frac{B}{P}$
(b) $\frac{P}{B}$
(c) $\frac{P D}{B}$
(d) $\frac{B D}{P}$

Dheeraj Sharma

Numerade Educator

Problem 3

For the same cross-sectional area and for a given load, the ratio of depression for the beam of a square cross-section and circular cross-section is
(a) $3: \pi$
(b) $\pi: 3$
(c) $1: 1$
(d) $1: \pi$

Dheeraj Sharma

Numerade Educator

Problem 4

A wire of length $L$ and cross-sectional area $A$ is made of a material of Young's modulus $Y$, if the wire is stretched by an amount $x$, the work done is
(a) $\frac{Y A x^{2}}{2 L}$
(b) $\frac{Y A x}{2 L^{2}}$
(c) $\frac{Y A x}{2 L}$
(d) $\frac{Y A x^{2}}{L}$

Dheeraj Sharma

Numerade Educator

Problem 5

One end of a uniform wire of length $L$ and of weight $W$ is attached rigidly to a point in the roof and a weight $W_{1}$ is suspended from its lower end. If $S$ is the area of crosssection of the wire, the stress in the wire at a height $3 L / 4$ from its lower end is
(a) $W_{1} / S$
(b) $\left(W_{1}+\frac{W}{4}\right) S$
(c) $\frac{\left(W_{1}+\frac{3 W}{4}\right)}{S}$
(d) $\left(W_{1}+W\right) S$

Dheeraj Sharma

Numerade Educator

Problem 6

A wire of radius $r$ stretched without tension along a straight line is lightly fixed at $A$ and $B$. What is the tension in the wire when it is pulled into the shape $A C B ?$ (Assume Young's modulus of the material of the wire to be $Y$ and $\bar{d}$ $<l$ )
(a) $\frac{Y d^{2}}{2 \pi r^{2} l^{2}}$
(b) $\frac{Y 2 \pi r^{2} d^{2}}{2 l^{2}}$
(c) $\frac{Y \pi r^{2}}{2 l^{2} d^{2}}$
(d) $\frac{Y \pi r^{2} l^{2}}{2 d^{2}}$

Dheeraj Sharma

Numerade Educator

Problem 7

One end of a steel wire is fixed to ceiling of an elevator moving up with an acceleration $2 \mathrm{~m} / \mathrm{s}^{2}$ and a load of 10 $\mathrm{kg}$ hangs from other end. Area of cross-section of the wire is $2 \mathrm{~cm}^{2}$. The longitudinal strain in the wire is $(g=$ $10 \mathrm{~m} / \mathrm{s}^{2}$ and $\left.Y=2 \times 10^{11} \mathrm{~N} / \mathrm{m}^{2}\right)$
(a) $4 \times 10^{11}$
(b) $3 \times 10^{-6}$
(c) $8 \times 10^{-6}$
(d) $2 \times 10^{-6}$

Dheeraj Sharma

Numerade Educator

Problem 8

Two bodies of masses $1 \mathrm{~kg}$ and $2 \mathrm{~kg}$ are connected by a metal wire shown in figure. A force of $10 \mathrm{~N}$ is applied on the body of mass $2 \mathrm{~kg}$. The breaking stress of metal wire is $2 \times 10^{9} \mathrm{~N} / \mathrm{m}^{2}$. What should be minimum radius of the wire used if it is not to break?
(a) $0.23 \times 10^{-4} \mathrm{~m}$
(b) $4 \times 10^{-4} \mathrm{~m}$
(c) $5 \times 10^{-4} \mathrm{~m}$
(d) $5.2 \times 10^{-4} \mathrm{~m}$

Dheeraj Sharma

Numerade Educator

Problem 9

The Young's modulus of brass and steel are respectively $10 \times 10^{10} \mathrm{~N} / \mathrm{m}^{2}$ and $2 \times 10^{10} \mathrm{~N} / \mathrm{m}^{2}$. A brass wire and a
steel wire of the same length are extended by $1 \mathrm{~mm}$ under the same force; the radii of brass and steel wires are $R_{B}$ and $R_{s}$ respectively. Then
(a) $R_{S}=\sqrt{2} R_{B}$
(b) $R_{s}=\frac{R_{B}}{\sqrt{2}}$
(c) $R_{s}=4 R_{B}$
(d) $R_{s}=\frac{R_{B}}{4}$

Dheeraj Sharma

Numerade Educator

Problem 10

Two wires of the same material (Young's modulus $Y$ ) and same length $L$ but radii $R$ and $2 R$ respectively are joined end to end and a weight $W$ is suspended from the combination as shown in the figure. The elastic potential energy in the system is
(a) $\frac{3 W^{2} L}{4 \pi R^{2} Y}$
(b) $\frac{3 W^{2} L}{8 \pi R^{2} Y}$
(c) $\frac{5 W^{2} L}{8 \pi R^{2} Y}$
(d) $\frac{W^{2} L}{\pi R^{2} Y}$

Dheeraj Sharma

Numerade Educator

Problem 11

A load suspended by a massless spring produces an extension of $x \mathrm{~cm}$ in equilibrium. When it is cut into two unequal parts, the same load produces an extension of $7.5 \mathrm{~cm}$ when suspended by the larger part of length $60 \mathrm{~cm} .$ When it is suspended by the smaller part, the extension is $5.0 \mathrm{~cm}$. Then
(a) $x=12.5$
(b) $x=3.0$
(c) the length of the original spring is $90 \mathrm{~cm}$
(d) the length of the original spring is $80 \mathrm{~cm}$

Dheeraj Sharma

Numerade Educator

Problem 12

One end of a long metallic wire of length $L$ is tied to the ceiling. The other end is tied to a massless spring of spring constant $k$. A mass $m$ hangs freely from the free end of the spring. The area of cross-section and the Young's modulus of the wire are $A$ and $Y$ respectively. Find the time period with which mass $m$ will oscillate if it is slightly pulled down and released
(a) $2 \pi \sqrt{\frac{A Y k}{m(A Y+k L)}}$
(b) $2 \pi \sqrt{\frac{m(A Y+k L)}{A Y k}}$
(c) $2 \pi \sqrt{\frac{Y k}{m A(A Y+k L)}}$
(d) None of these

Dheeraj Sharma

Numerade Educator

Problem 13

A solid sphere of radius $R$, made of material of bulk modulus $B$, is surrounded by a liquid in a cylindrical container. A massless piston of area $A$ floats on the surface of the liquid. When a mass $M$ is placed on the piston to compress the liquid, the fractional change in the radius of the sphere is
(a) $\frac{M g}{B A}$
(b) $\frac{M g}{3 B A}$
(c) $\frac{3 M g}{4 B A}$
(d) $\frac{M g}{4 B A R}$

Dheeraj Sharma

Numerade Educator

Problem 14

A steel wire is suspended vertically from a rigid support. When loaded with a weight in air, it extends by $l_{a}$ and when the weight is immersed completely in water, the extension is reduced to $l_{w}$. Then the relative density of the material of the weight is
(a) $\frac{l_{a}}{l_{w}}$
(b) $\frac{l_{a}}{l_{a}-l_{w}}$
(c) $\frac{l_{w}}{l_{a}-l_{w}}$
(d) $\frac{l_{m}}{l_{a}}$

Dheeraj Sharma

Numerade Educator

Problem 15

A block of weight $W$ produces an extension of $9 \mathrm{~cm}$ when it is hung by an elastic spring of length $60 \mathrm{~cm}$ and is in equilibrium. The spring is cut into two parts, one of length $40 \mathrm{~cm}$ and the other of length $20 \mathrm{~cm}$. The same load $W$ hangs in equilibrium supported by both parts as shown in Fig. The extension (in $\mathrm{cm}$ ) now is
(a) 9
(b) 6
(c) 3
(d) 2

Dheeraj Sharma

Numerade Educator

Problem 16

A material has Poisson's ratio $0.50$. If a uniform rod of it suffers a longitudinal strain of $2 \times 10^{-3}$, then the percentage change in volume is
(a) $0.6$
(b) $0.4$
(c) $0.2$
(d) zero

Dheeraj Sharma

Numerade Educator

Problem 17

The Poisson's ratio of a material is $0.4$. If a force is applied to a wire of this material, there is a decrease of cross-sectional area by $2 \%$. the percentage increase in its length is
(a) $3 \%$
(b) $2.5 \%$
(c) $1 \%$
(d) $0.5 \%$

Dheeraj Sharma

Numerade Educator

Problem 18

A metal wire is first stretched beyond its elastic limit and then released. It
(a) loses its elastic property completely and it will not contract.
(b) will contract to its original length.
(c) will contract to its length at elastic limit.
(d) will contract but final length will be greater than original length.

Dheeraj Sharma

Numerade Educator

Problem 19

A uniform solid cylinder made of steel, is compressed along the axis. Which of the following statements is correct?
(a) Decrease in volume of the cylinder is independent of its area of cross-section but directly proportional to its length.
(b) Decrease in volume of the cylinder is independent of its area of cross-section but inversely proportional to its length.
(c) Decrease in volume of the cylinder is directly proportional to its cross-sectional area but is independent of its length
(d) Decrease in volume of the cylinder is inversely proportional to its volume as well as length.

Dheeraj Sharma

Numerade Educator

Problem 20

A rod of length $l$ and radius $r$ is joined to a rod of length $\frac{l}{2}$ and radius $\frac{r}{2}$ of same material. The free end of small rod is fixed to a rigid base and free end of large rod is given a twist of $\theta_{e}$, the twist angle at the joint will be
(a) $\frac{\theta}{4}$
(b) $\frac{\theta}{2}$
(c) $\frac{5 \theta}{6}$
(d) $\frac{8 \theta}{9}$

Dheeraj Sharma

Numerade Educator

Problem 21

The pressure applied from all directions on a cube is $P$. How much its temperature should be raised to maintain the original volume? (The volume elasticity of the cube is $\beta$ and the coefficient of volume expansion is $\alpha$ )
(a) $\frac{P}{\alpha \beta}$
(b) $\frac{P \alpha}{\beta}$
(c) $\frac{P \beta}{\alpha}$
(d) $\frac{\alpha \beta}{P}$

Dheeraj Sharma

Numerade Educator

Problem 22

The potential energy $U$ between two atoms in a diatomic molecule as a function of the distance $x$ between atoms has been shown in the adjoining figure. The atoms are
(a) attracted when $x$ lies between $A$ and $B$ are repelled when $x$ lies between $B$ and $C$
(b) attracted when $x$ lies between $B$ and $C$ and are repelled when $x$ lies between $A$ and $B$
(c) attracted when they reach $B$
(d) repelled when they reach $B$

Dheeraj Sharma

Numerade Educator

Problem 23

If the ratio of lengths, radii and Young's modulus of steel and brass wires in the figure are $a, b$ and $c$ respectively, then the corresponding ratio of increase in their lengths would be
(a) $\frac{2 a^{2} c}{b}$
(b) $\frac{3 a}{2 b^{2} c}$
(c) $\frac{2 a c}{b^{2}}$
(d) $\frac{3 c}{2 a b^{2}}$

Dheeraj Sharma

Numerade Educator

Problem 24

A wire elongates by $l \mathrm{~mm}$ when a load $W$ is hanged from it. If the wire goes over a pulley and two weights $W$ each are hung at the two ends, the elongation of the wire will be (in $\mathrm{mm}$ )
(a) $l / 2$
(b) $l$
(c) $2 l$
(d) zero

Dheeraj Sharma

Numerade Educator

Problem 25

A work of $2 \times 10^{-2} \mathrm{~J}$ is done on a wire of length $50 \mathrm{~cm}$ and area of cross-section $0.5 \mathrm{~mm}^{2}$. If the Young's modulus of the material of the wire is $2 \times 10^{10} \mathrm{~N} / \mathrm{m}^{2}$, then the wire must be
(a) elongated to $50.1414 \mathrm{~cm}$
(b) contracted by $2.0 \mathrm{~mm}$
(c) stretched by $0.707 \mathrm{~mm}$
(d) None of these

Dheeraj Sharma

Numerade Educator

Problem 26

When a spring is stretched by a distance $x$, it exerts a force, given by $F=\left(-5 x-16 x^{3}\right) \mathrm{N}$. The work done, when the spring is stretched from $0.1 \mathrm{~m}$ to $0.2 \mathrm{~m}$ is
(a) $8.7 \times 10^{-2} \mathrm{~J}$
(b) $12.2 \times 10^{-2} \mathrm{~J}$
(c) $8.7 \times 10^{-1} \mathrm{~J}$
(d) $12.2 \times 10^{-1} \mathrm{~J}$

Dheeraj Sharma

Numerade Educator

Problem 27

The strain-stress curves of three wires of different materials are shown in the figure. $P, Q$ and $R$ are the elastic limits of the wires. The figure shows that
(a) elasticity of wire $P$ is maximum
(b) elasticity of wire $Q$ is maximum
(c) tensile strength of $R$ is maximum
(d) None of these

Dheeraj Sharma

Numerade Educator

Problem 28

A particle of mass $m$ under the influence of a force $F$ which varies with the displacement $x$ according to the relation $F=-k x+F_{o}$, in which $k$ and $F_{\text {ore constants. }}$ The particle when disturbed will oscillate
(a) about $x=0$ with $\omega \neq \sqrt{\frac{k}{m}}$
(b) about $x=0$ with $\omega=\sqrt{\frac{k}{m}}$
(c) about $x=\frac{F_{0}}{k}$ with $\omega=\sqrt{\frac{k}{m}}$
(d) about $x=\frac{F_{0}}{k}$ with $\omega \neq \sqrt{\frac{k}{m}}$

Dheeraj Sharma

Numerade Educator

Problem 29

The graph shown was obtained from experimental measurements of the period of oscillations $T$ for different masses $M$ placed in the scale pan on the lower end of spring balance. The most likely reason for the line not passing through the origin is that the
(a) spring did not obey Hooke's law
(b) amplitude of the oscillations was too large
(c) clock used needed regulating
(d) mass of the pan was neglected

Dheeraj Sharma

Numerade Educator

Problem 30

The stress versus strain graphs for wires of two materials $A$ and $B$ are as shown in the figure. If $Y_{A}$ and $Y_{B}$ are the Young's modulii of the materials, then
(a) $Y_{B}=2 Y_{A}$
(b) $Y_{A}=Y_{B}$
(c) $Y_{B}=3 Y_{A}$
(d) $Y_{A}=3 Y_{B}$

Dheeraj Sharma

Numerade Educator

Problem 31

The diagram shows a force extension graph for a rubber band. Consider the following statements
I. It will be easier to compress this rubber than expand it.
II. Rubber does not return to its original length after it stretched.
III. The rubber band will get heated if it is stretched and released.
Which of these can be deduced from the graph?
(a) III only
(b) II and III
(c) I and III
(d) I only

Dheeraj Sharma

Numerade Educator

Problem 32

Which one of the following statements is wrong?
(a) Young's modulus for a perfectly rigid body is zero.
(b) Bulk modulus is relevant for solids, liquids and gases.
(c) Rubber is less elastic than steel.
(d) The Young's modulus and shear modulus are relevant for solids.

Dheeraj Sharma

Numerade Educator

Problem 33

The points of maximum and minimum attraction in the curve between potential energy $(U)$ and distance $(r)$ of a diatomic molecule are respectively
(a) $S$ and $R$
(b) $T$ and $S$
(c) $R$ and $S$
(d) $S$ and $T$

Dheeraj Sharma

Numerade Educator

Problem 34

Bulk modulus of water is $2 \times 10^{5} \mathrm{~N} / \mathrm{m}^{2}$. The change in pressure required to increase density of water by $0.1 \%$ is
(a) $2 \times 10^{9} \mathrm{~N} / \mathrm{m}^{2}$
(b) $2 \times 10^{8} \mathrm{~N} / \mathrm{m}^{2}$
(c) $2 \times 10^{6} \mathrm{~N} / \mathrm{m}^{2}$
(d) $2 \times 10^{4} \mathrm{~N} / \mathrm{m}^{2}$

Dheeraj Sharma

Numerade Educator

Problem 35

A thin walled circular tube of mean radius $8 \mathrm{~cm}$ and thickness $0.04 \mathrm{~cm}$ is melted up and recast into a solid rod of the same length. The ratio of their torsional rigidities in the two cases is
(a) $\frac{C_{H}}{C_{s}}=\frac{(8.04)^{4}-(7.96)^{4}}{(8)^{4}}$
(b) $\frac{C_{H}}{C_{s}}=\frac{(8.02)^{4}-(7.98)^{4}}{(8)^{4}}$
(c) $\frac{C_{H}}{C_{s}}=\frac{(8.02)^{4}-(7.98)^{4}}{(0.8)^{4}}$
(d) $\frac{C_{H}}{C_{s}}=\frac{(8.04)^{4}-(7.96)^{4}}{(0.8)^{4}}$

Dheeraj Sharma

Numerade Educator

Problem 36

A uniform plank is resting over a smooth horizontal floor and is pulled by applying a horizontal force at its one end. Which of the following statements is correct?
(a) Stress developed in plank material is maximum at the end at which force is applied and decreases linearly to zero at the other end.
(b) A uniform tensile stress is developed in the plank material.
(c) Since the plank is pulled at one end only, therefore it starts to accelerate along the direction of the force. Hence, no stress is developed in the plank material.
(d) None of these

Dheeraj Sharma

Numerade Educator

Problem 37

If the pressure of gas is increased from $1.01 \times 10^{5} \mathrm{~Pa}$ to $1.165 \times 10^{5} \mathrm{~Pa}$ and volume is decreased by $10 \%$ at constant temperature, then the bulk modulus of the gas is
(a) $15.5 \times 10^{5} \mathrm{~Pa}$
(b) $1.4 \times 10^{5} \mathrm{~Pa}$
(c) $1.55 \times 10^{5} \mathrm{~Pa}$
(d) $0.0155 \times 10^{5} \mathrm{~Pa}$

Dheeraj Sharma

Numerade Educator

Problem 38

The angle of contact of a liquid surface with a solid surface is $90^{\circ}$, when
(a) $F_{A}<\frac{F_{C}}{\sqrt{2}}$
(b) $F_{A}=\frac{F_{C}}{\sqrt{2}}$
(c) $F_{A}>\frac{F_{c}}{\sqrt{2}}$
(d) $F_{A}>F_{C}$

Dheeraj Sharma

Numerade Educator

Problem 39

If $F_{C}$ and $F_{A}$ denote cohesive and adhesive forces on a liquid molecule near the surface of a solid, then the surface of liquid is concave, when
(a) $F_{A}<\frac{F_{c}}{\sqrt{2}}$
(b) $F_{A}=\frac{F_{C}}{\sqrt{2}}$
(c) $F_{A}>\frac{F_{c}}{\sqrt{2}}$
(d) $F_{A}>F_{C}$

Dheeraj Sharma

Numerade Educator

Problem 40

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

Dheeraj Sharma

Numerade Educator

Problem 41

Two soap bubbles, each with radius $r$, coalesce in vacuum under isothermal conditions to form a bigger bubble of radius $R$. Then $R$ is equal to
(a) $2^{-1 / 2} r$
(b) $2^{1 / \beta} r$
(c) $2^{1 / 2} r$
(d) $2 r$

Dheeraj Sharma

Numerade Educator

Problem 42

A soap bubble of radius $r_{1}$ is placed on another soap bubble of radius $r_{2}\left(r_{1}<r_{2}\right)$. The radius $R$ of the soapy film separating the two bubbles is
(a) $r_{1}+r_{2}$
(b) $\sqrt{r_{1}^{2}+r_{2}^{2}}$
(c) $\left(r_{1}^{3}+r_{2}^{3}\right)^{1 / 3}$
(d) $\frac{r_{2} r_{1}}{r_{2}-r_{1}}$

Dheeraj Sharma

Numerade Educator

Problem 43

If two soap bubbles of different radii are in communication with each other
(a) air flows from larger bubble into the smaller one until the two bubbles are of equal size.
(b) the sizes of the bubbles remain the same.
(c) air flows from the smaller bubble into the larger one and larger bubble grows at the expense of the smaller one.
(d) the air flows from the larger bubble into the smaller bubble until the radius of the smaller one becomes equal to that of the larger one and of the larger one equal to that of the smaller one.

Dheeraj Sharma

Numerade Educator

Problem 44

A number of water droplets each of radius $r$ coalesce to form a drop of radius $R$. Assuming the whole of the energy liberated due to coalescence goes into heating the drop, the rise in the temperature $d \theta$ is
(a) $\frac{2 T}{r J}$
(b) $\frac{3 T}{r J}$
(c) $\frac{3 T}{J}\left(\frac{1}{r}-\frac{1}{R}\right)$
(d) $\frac{3 T}{J}\left(\frac{1}{r}+\frac{1}{R}\right)$

Dheeraj Sharma

Numerade Educator

Problem 45

The height upto which water will rise in capillary tube will be
(a) same at all temperatures
(b) minimum when temperature of water is $0^{\circ} \mathrm{C}$
(c) maximum when temperature of water is $4^{\circ} \mathrm{C}$
(d) minimum when temperature of water is $4^{\circ} \mathrm{C}$

Dheeraj Sharma

Numerade Educator

Problem 46

Liquid rises to a height of $2 \mathrm{~cm}$ in a capillary tube. The angle of contact between the solid and the liquid is zero. The tube is depressed more now so that the top of the capillary is only $1 \mathrm{~cm}$ above the liquid. Then the apparent angle of contact between the solid and the liquid is
(a) $0^{\circ}$
(b) $30^{\circ}$
(c) $60^{\circ}$
(d) $90^{\circ}$

Dheeraj Sharma

Numerade Educator

Problem 47

What will happen if $n$ drops of a liquid, each having surface energy $E$, combine to form a single drop?
(a) No energy will be released in the process.
(b) Some energy will be absorbed in the process.
(c) Energy released or absorbed will be $E\left(n-n^{2 / 3}\right)$.
(d) Energy released or absorbed will be $n E\left(n^{2 / 3}-1\right)$.

Dheeraj Sharma

Numerade Educator

Problem 48

Liquid reaches an equilibrium as shown, in a capillary tube of internal radius $r$. If the surface tension of the liquid is $T$, the angle of contact $\theta$ and density of liquid $\rho$, then the pressure difference between $P$ and $Q$ is
(a) $\left(\frac{2 T}{r}\right) \cos \theta$
(b) $\frac{T}{r \cos \theta}$
(c) $\frac{2 T}{r \cos \theta}$
(d) $\left(\frac{4 T}{r}\right) \cos \theta$

Dheeraj Sharma

Numerade Educator

Problem 49

Water rises to a height of $10 \mathrm{~cm}$ in a capillary tube and mercury falls to a depth of $3.42 \mathrm{~cm}$ in the same capillary tube. If the density of mercury is $13.6$ and angle of contact is $135^{\circ}$, the ratio of surface tension for water and mercury is (Angle of contact for water and glass is $8^{\circ}$ )
(a) $1: 0.5$
(b) $1: 3$
(c) $1: 6.5$
(d) $1.5: 1$

Dheeraj Sharma

Numerade Educator

Problem 50

1000 drops of water all of same size join together to form a single drop and the energy released raises the temperature of the drop. Given that $T$ is the surface tension of water, $r$ the radius of each small drop, $\rho$ the density of liquid, $J$ the mechanical equivalent of heat. What is the rise in temperature?
(a) $T / J r$
(b) $10 \mathrm{~T} / \mathrm{Jr}$
(c) $100 \mathrm{~T} / \mathrm{Jr}$
(d) None of these

Dheeraj Sharma

Numerade Educator

Problem 51

A large number of liquid drops each of radius $r$ coalesce to form a single drop of radius $R$. The energy released in the process is converted into the kinetic energy of the big drop so formed. The speed of the big drop is (Given surface tension of liquid is $T$, density of liquid is $\rho$ )
(a) $\sqrt{\frac{T}{\rho}\left(\frac{1}{r}-\frac{1}{R}\right)}$
(b) $\sqrt{\frac{2 T}{\rho}\left(\frac{1}{r}-\frac{1}{R}\right)}$
(c) $\sqrt{\frac{4 T}{\rho}\left(\frac{1}{r}-\frac{1}{R}\right)}$
(d) $\sqrt{\frac{6 T}{\rho}\left(\frac{1}{r}-\frac{1}{R}\right)}$

Dheeraj Sharma

Numerade Educator

Problem 52

Which graph represents the variation of surface tension with temperature over small temperature ranges for water?
(a)
(b)
(c)
(d)

Dheeraj Sharma

Numerade Educator

Problem 53

A soap bubble is blown with the help of a mechanical pump at the mouth of a tube. The pump produces a certain increase per minute in the volume of the bubble, irrespective of its internal pressure. The graph between the pressure inside the soap bubble and time $t$ will be
(a)
(b)
(c)
(d)

Dheeraj Sharma

Numerade Educator

Problem 54

The height upto which water will rise in a capillary tube will be
(a) maximum when water temperature is $4{ }^{\circ} \mathrm{C}$
(b) maximum when water temperature is $0^{\circ} \mathrm{C}$
(c) minimum when water temperature is $4{ }^{\circ} \mathrm{C}$
(d) same at all temperatures

Dheeraj Sharma

Numerade Educator

Problem 55

Two parallel glass plates are dipped partly in the liquid of density $d$ keeping them vertical. If the distance between the plates is $x$, surface tension for liquids is $T$ and angle of contact is $\theta$, then rise of liquid between the plates due to capillary will be
(a) $\frac{T \cos \theta}{x d}$
(b) $\frac{2 T \cos \theta}{x d g}$
(c) $\frac{2 T}{x d g \cos \theta}$
(d) $\frac{T \cos \theta}{x d g}$

Dheeraj Sharma

Numerade Educator

Problem 56

The parallel glass plates having separation $d$ are dipped in water. Some water rises up in the gap between the plates. The surface tension of water is $T$, atmospheric pressure is $P_{o}$, pressure of water just below the water surface in the region between the plates is $P$. Find the relation between $P, P_{o}, T$ and $d$
(a) $P=P_{o}-\frac{2 T}{d}$
(b) $P=P_{o}+\frac{2 T}{d}$
(c) $P=P_{o}-\frac{4 T}{d}$
(d) $P=P_{o}+\frac{4 T}{d}$

Dheeraj Sharma

Numerade Educator

Problem 57

Two spherical soap bubbles of radii $r_{1}$ and $r_{2}$ in vacuum combine under isothermal conditions. The resulting bubble has a radius equal to
(a) $\frac{r_{1}+r_{2}}{2}$
(b) $\sqrt{r_{1}+r_{2}}$
(c) $\frac{r_{1} r_{2}}{r_{1}+r_{2}}$
(d) $\sqrt{r_{1}^{2}+r_{2}^{2}}$

Dheeraj Sharma

Numerade Educator

Problem 58

The work done in increasing the size of a rectangular soap film with dimensions $8 \mathrm{~cm} \times 3.75 \mathrm{~cm}$ to $10 \mathrm{~cm} \times 6$ $\mathrm{cm}$ is $2 \times 10^{-4} \mathrm{~J}$. The surface tension of the film in $\mathrm{N} / \mathrm{m}$ is
(a) $1.65 \times 10^{-2}$
(b) $3.3 \times 10^{-2}$
(c) $6.6 \times 10^{-2}$
(d) $8.25 \times 10^{-2}$

Dheeraj Sharma

Numerade Educator

Problem 59

In a capillary tube experiment, a vertical $30 \mathrm{~cm}$ long capillary tube is dipped in water. The water rises upto a height of $10 \mathrm{~cm}$ due to capillary action. If this experiment is conducted in a freely falling elevator, the length of the water column becomes
(a) $10 \mathrm{~cm}$
(b) $20 \mathrm{~cm}$
(c) $30 \mathrm{~cm}$
(d) zero

Dheeraj Sharma

Numerade Educator

Problem 60

If the length of tube is less and cannot accommodate the maximum rise of liquid, then
(a) liquid will form a fountain
(b) liquid will not rise
(c) the meniscus will adjust itself so that the water does not spill
(d) None of these

Dheeraj Sharma

Numerade Educator