Objective Physics : NEET 2020 Examination textbook Gurukul Oswal

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Chapter 7

PROPERTIES OF BULK MATTER - all with Video Answers

Educators

Section 1

Mechanical Properties of Solids

Problem 1

A boy have two identical solid balls, one of ivory and the other of wet clay are dropped from the same height on the floor. After striking the floor:(a) ivory ball will rise to a greater height than wet clay ball.
(b) ivory ball will rise to a lesser height than wet clay ball.
(c) both balls will rise to the same height.
(d) None of these

Ajay Singhal

Ajay Singhal

Numerade Educator

Problem 2

What is the nature of intermolecular forces?
(a) Always attractive
(b) Always repulsive
(c) Attractive and repulsive both depend on the intermolecular separation
(d) Data is insufficient

Narayan Hari

Numerade Educator

Problem 3

A body of mass $m=10 \mathrm{~kg}$ is attached to a wire of length $0.3 \mathrm{~m}$. The maximum angular velocity with which it can be rotated in a horizontal circle is (Tensile or breaking stress of wire $=4.8 \times 10^{7} \mathrm{Nm}^{-2}$ and area of cross-section of wire $=10^{-6} \mathrm{~m}^{2}$ ):
(a) $4 \mathrm{rad} / \mathrm{s}$
(b) $8 \mathrm{rad} / \mathrm{s}$
(c) $2 \mathrm{rad} / \mathrm{s}$
(d) $1 \mathrm{rad} / \mathrm{s}$

Narayan Hari

Numerade Educator

Problem 4

The breaking stress for a copper wire is $2.2 \times 10^{8} \mathrm{Nm}^{-2}$. The maximum length of the copper wire which when suspended vertically for which the wire will not break under its own weight, will be: (Density of copper $=8.8 \times 10^{3} \mathrm{kgm}^{-3}$ )
(a) $25000 \mathrm{~m}$
(b) $2500 \mathrm{~m}$
(c) $250 \mathrm{~m}$
(d) $25 \mathrm{~m}$

Narayan Hari

Numerade Educator

Problem 5

Which of the following statements is incorrect?
(a) When a material is under tensile stress, the restoring forces are caused by interatomic attraction while under compressional stress; the restoring force is due to interatomic repulsion.
(b) The stretching of a coil is determined by its shear modulus.
(c) Rubber is more elastic than steel.
(d) Shearing stress plays an important role in the buckling of shafts.

Narayan Hari

Numerade Educator

Problem 6

Shape is related to:
(a) Shear stress
(b) Shear strain
(c) Breaking stress
(d) Poisson's ratio

Narayan Hari

Numerade Educator

Problem 7

Only volumetric strain can be developed in case of:
(a) Fluid and solid
(b) Solid
(c) Fluid
(d) All of the above

Narayan Hari

Numerade Educator

Problem 8

Stress is a quantity.
(a) Vector
(b) Scalar
(c) Dimensionless
(d) Tensor

Kamlesh Goyal

Numerade Educator

Problem 9

The tensile stress of a wire depends upon:
(a) Length of the wire
(b) Radius of the wire
(c) Shape of the cross-section of the wire
(d) Nature of the material of the wire

Narayan Hari

Numerade Educator

Problem 10

A wire is suspended from the ceiling and stretched under the action of a weight $F / 2$ suspended from its other end. The force exerted by the ceiling on it is equal and opposite to the weight.
(a) Tensile stress at any cross-section $A$ of the wire
is $\underline{F}$(b) Tensile stress at any cross-section is zero.
(c) Tensile stress at any cross-section $A$ of the wire is $\frac{F}{2 A}$
(d) Tension at any cross-section $A$ of the wire is $2 F$.

Ajay Singhal

Numerade Educator

Problem 11

The expression of force constant for a spring following Hooke's law is given by:
(a) $k=\frac{Y A}{l}$
(b) $k=\frac{Y A}{\Delta l}$
(c) $k=\frac{Y A \Delta l}{l}$
(d) $k=\frac{Y A l}{\Delta l}$

Narayan Hari

Numerade Educator

Problem 12

If the length of a wire is reduced to half then it can hold the:
(a) Half load
(b) Same load
(c) Double load
(d) One-fourth load

Narayan Hari

Numerade Educator

Problem 13

'According to Hookes law of elasticity, if stress is increased, then the ratio of stress to strain:
(a) Becomes zero
(b) Remains constant
(c) Decreases
(d) Increases

Narayan Hari

Numerade Educator

Problem 14

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 is 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

Ajay Singhal

Numerade Educator

Problem 15

A $2 \mathrm{~m}$ long rod of radius $1 \mathrm{~cm}$ which is fixed from one end is given a force of $8 \mathrm{~N}$. The longitudinal strain developed will be:[Take $\left.Y=2.5 \times 10^{11} \mathrm{Nm}^{-2}\right]$
(a) $10^{-8}$
(b) $10^{-7}$
(c) $10^{-5}$
(d) $10^{-4}$

Narayan Hari

Numerade Educator

Problem 16

In which year Robert Hooke presented his law of elasticity?
(a) 1672
(b) 1674
(c) 1676
(d) 1678

Kamlesh Goyal

Numerade Educator

Problem 17

If stress is increased, the ratio of strain to stress:
(a) Increases
(b) Decreases
(c) Remains constant
(d) Becomes zero

Narayan Hari

Numerade Educator

Problem 18

Within elastic limit, which of the following graphs correctly represents the variation of extension in the length of a wire with the external load?(a) (i)
(b) (ii)
(c) (iii)
(d) (iv)

Narayan Hari

Numerade Educator

Problem 19

The restoring force per unit area is known as:
(a) Strain
(b) Elasticity
(c) Stress
(d) Plasticity

Narayan Hari

Numerade Educator

Problem 20

In magnitude hydraulic stress is equal to:
(a) Hydraulic force
(b) Hydraulic pressure
(c) Restoring force
(d) Hydraulic strain

Narayan Hari

Numerade Educator

Problem 21

Substances which can be stretched to cause large strains are called:
(a) Brittle
(b) Ductile
(c) Plastic
(d) Elastomer

Narayan Hari

Numerade Educator

Problem 22

Longitudinal stress depends on:
(a) Area
(b) Length
(c) Volume
(d) Mass

Narayan Hari

Numerade Educator

Problem 23

The breaking stress for a wire of unit cross-section is called:
(a) Yield point
(b) Elastic fatigue
(c) Tensile strength
(d) Young's modulus

Kamlesh Goyal

Numerade Educator

Problem 24

A wire is stretched through $1 \mathrm{~mm}$ by certain load. The extension produced in the wire of same material with double the length and double the radius will be:
(a) $0.5 \mathrm{~mm}$
(b) $1 \mathrm{~mm}$
(c) $1.5 \mathrm{~mm}$
(d) $2 \mathrm{~mm}$

Narayan Hari

Numerade Educator

Problem 25

A $10 \mathrm{~m}$ long thick rubber pipe is suspended from one of its ends. The extension produced in the pipe under its own weight will be ( $Y=5 \times 10^{6} \mathrm{Nm}^{-2}$ and density of rubber $=1500 \mathrm{kgm}^{-3}$ )
(a) $1.5 \mathrm{~m}$
(b) $0.15$
(c) $0.015$
(d) $0.0015$

Narayan Hari

Numerade Educator

Problem 26

If $\mathrm{G}=$ shear modulus and $Y=$ Young's modulus, then in general:
(a) $\mathrm{Y}>\mathrm{G}$
(b) $\mathrm{Y}=\mathrm{G}$
(c) $\mathrm{Y}<\mathrm{G}$
(d) Data is insufficient

Ajay Singhal

Numerade Educator

Problem 27

Which of the following affects the elasticity of a substance?
(a) Hammering and annealing
(b) Change in temperature
(c) Impurity in substance
(d) All of the above

Ajay Singhal

Numerade Educator

Problem 28

The stress-strain graph for a metal wire is as shown in the figure. In the graph, the region in which Hooke's law is obeyed, the ultimate strength and fracture points are represented by:(a) $\mathrm{OP}, \mathrm{R}, \mathrm{S}$
(b) $\mathrm{OQ}, \mathrm{S}, \mathrm{T}$
(c) $\mathrm{OP}, \mathrm{S}, \mathrm{T}$
(d) $\mathrm{OQ}, \mathrm{R}, \mathrm{S}$

Ajay Singhal

Numerade Educator

Problem 29

Which of the following graphs represents stressstrain variation for elastomers?(a) (i)
(b) (ii)
(c) (iii)
(d) (iv)

Narayan Hari

Numerade Educator

Problem 30

A copper wire ( $Y=1 \times 10^{11} \mathrm{Nm}^{-2}$ ) of length $6 \mathrm{~m}$ and a steel wire $\left(Y=2 \times 10^{11} \mathrm{Nm}^{-2}\right)$ of length $4 \mathrm{~m}$ each of cross-section $10^{-5} \mathrm{~m}^{2}$ are fastened end to end and stretched by a tension of $100 \mathrm{~N}$. The elongation produced in the copper wire is:
(a) $0.2 \mathrm{~mm}$
(b) $0.4 \mathrm{~mm}$
(c) $0.6 \mathrm{~mm}$
(d) $0.8 \mathrm{~mm}$

Narayan Hari

Numerade Educator

Problem 31

If the load is increased beyond the point, the strain increases rapidly for even a small change in the stress.
(a) elastic point
(b) yield point
(c) plastic point
(d) fracture point

Narayan Hari

Numerade Educator

Problem 32

What is the phenomenon of temporary delay in regaining the original configuration by an elastic body, after the removal of a deforming force?
(a) elastic fatigue
(b) elasticity
(c) plasticity
(d) elastic after effect

Narayan Hari

Numerade Educator

Problem 33

Which of the following types of stress causes no change in shape?
(a) Compressive stress
(b) Hydraulic stress
(c) Oblique stress
(d) None of these

Narayan Hari

Numerade Educator

Problem 34

Which of the following statements is incorrect?
(a) Young's modulus and shear modulus are relevant only for solids.
(b) Bulk modulus is relevant for solids, liquids, and gases.
(c) Metals have larger values of Young's modulus than elastomers.
(d) Alloys have larger values of Young's modulus than metals.

Kamlesh Goyal

Numerade Educator

Problem 35

If a mass $M$ produces an elongation of $\Delta L$ in a wire of radius $r$ and length $L$, then the Young's modulus of the material of the wire is given by:
(a) $Y=\frac{M g}{\left(\pi r^{2} \times \Delta L\right)}$
(b) $Y=\frac{M g \times \Delta L}{\left(\pi r^{2} \times L\right)}$
(c) $Y=\frac{M g \times L}{\left(\pi r^{2} \times \Delta L\right)}$
(d) $Y=\frac{M \times \Delta L}{\left(\pi r^{2} \times L\right)}$

Narayan Hari

Numerade Educator

Problem 36

A vertical metal cylinder of radius $2 \mathrm{~cm}$ and length $2 \mathrm{~m}$ is fixed at the lower end and a load of $100 \mathrm{~kg}$ is put on it. Find the strain: [Young's modulus of the metal $\left.=2 \times 10^{11} \mathrm{Nm}^{-2}\right]$
(a) $4 \times 10^{-6}$
(b) $3 \times 10^{-8}$
(c) $2 \times 10^{-9}$
(d) $6 \times 10^{-8}$

Narayan Hari

Numerade Educator

Problem 37

A vertical metal cylinder of radius $2 \mathrm{~cm}$ and length $2 \mathrm{~m}$ is fixed at the lower end and a load of $80 \mathrm{~kg}$ is put on it. Find the strain: [Young's modulus of the metal $\left.=2 \times 10^{11} \mathrm{Nm}^{-2}\right]$
(a) $4.18 \times 10^{-6}$
(b) $3.18 \times 10^{-6}$
(c) $2.18 \times 10^{-9}$
(d) $6.18 \times 10^{-8}$

Narayan Hari

Numerade Educator

Problem 38

Match the following with correct one.$$
\begin{aligned}
&\begin{array}{llll}
\text { A } & \begin{array}{l}
\text { Equal force acting } \\
\text { perpendicular to }
\end{array} & \text { (i) } & \begin{array}{l}
\text { Balance the net } \\
\text { weight to be sup- } \\
\text { each point on a } \\
\text { spherical surface }
\end{array} & & \text { ported } \\
\hline \text { B } & \begin{array}{l}
\text { Cross-sectional } \\
\text { area of the rope }
\end{array} & \text { (ii) } & \begin{array}{l}
\text { Higher modulus } \\
\text { used in giant } \\
\text { of elasticity }
\end{array} \\
& \text { structures } & & \\
\hline \text { C } & \begin{array}{l}
\text { Steel in structural } \\
\text { designs }
\end{array} & \text { (iii) } & \begin{array}{l}
\text { Reduction in } \\
\text { volume without } \\
\text { change in shape }
\end{array} \\
& & &
\end{array}\\
&6
\end{aligned}
$$$$
\begin{array}{llll}
\hline \text { D } & \text { Stress-strain curve } & \text { (iv) } & \begin{array}{l}
\text { Inversely depends } \\
\text { on the yield } \\
\text { strength }
\end{array} \\
\hline
\end{array}
$$(a) A-(iii), B-(i), iv), C-(ii), D-(ii)
(b) $\mathrm{A}-(\mathrm{ii}), \mathrm{B}-(\mathrm{iii}), \mathrm{C}-(\mathrm{i}), \mathrm{D}-(\mathrm{iv})$
(c) A-(iii), B-(i, ii) C-(iii), (iv), D-(ii)
(d) A-(iv), B-(iii), C-(ii), D-(i)

Ajay Singhal

Numerade Educator

Problem 39

If the ratio of radii of two wires of same material is $3: 1$ and ratio of their lengths is $5: 1$, then the ratio of the normal forces that will produce the same extension in the length of two wires is:
(a) $2: 1$
(b) $4: 1$
(c) $1: 4$
(d) $1: 1$

Narayan Hari

Numerade Educator

Problem 40

For a perfectly rigid body:
(a) Young's modulus is infinite and bulk modulus is zero.
(b) Young's modulus is zero and bulk modulus is infinite.
(c) Young's modulus is infinite and bulk modulus is also infinite.
(d) Young's modulus is zero and bulk modulus is also zero.

Kamlesh Goyal

Numerade Educator

Problem 41

An iron bar of length $l \mathrm{~cm}$ and cross-section $A \mathrm{~cm}^{2}$ is pulled by a force of $F$ dynes from ends so as to produce an elongation $\Delta l \mathrm{~cm} .$ Which of the following statement is correct?
(a) Elongation is inversely proportional to length.
(b) Elongation is directly proportional to cross-section A.
(c) Elongation is inversely proportional to crosssection.
(d) Elongation is directly proportional to Young's modulus.

Narayan Hari

Numerade Educator

Problem 42

If the tension on a wire is removed at once, then:
(a) it will break.
(b) its temperature will reduce.
(c) there will be no change in its temperature.
(d) its temperature increases.

Narayan Hari

Numerade Educator

Problem 43

Two wires of equal lengths are made of the same material. Wire A has a diameter that is twice as that of wire B. If identical weights are suspended from the ends of these wires, the increase in length is:
(a) four times for wire $\mathrm{A}$ as for wire $\mathrm{B}$.
(b) twice for wire $\mathrm{A}$ as for wire $\mathrm{B}$.
(c) half for wire $\mathrm{A}$ as for wire $\mathrm{B}$.
(d) one-fourth for wire $\mathrm{A}$ as for wire $\mathrm{B}$.

Ajay Singhal

Numerade Educator

Problem 44

Steel ring of radius rand cross-section area $A$ is fitted on to a wooden disc of radius $R(R>r) .$ If Young's modulus be $E$, then the force with which the steel ring is expanded is:(a) $A E \frac{R}{r}$
(b) $A E \frac{(R-r)}{r}$
(c) $\frac{E(R-r)}{A} \frac{(R-r)}{r}$
(d) $\frac{E}{A} \frac{r}{R}$

Narayan Hari

Numerade Educator

Problem 45

Two persons pull a rope towards themselves. Each person exerts a force of $100 \mathrm{~N}$ on the rope. Find the Young's modulus of the material of the rope if it extends in length by $1 \mathrm{~cm}$. Original length of the rope $=2 \mathrm{~m}$ and the area of cross-section $=2 \mathrm{~cm}^{2}$
(a) $10^{8} \mathrm{Nm}^{-2}$
(b) $10^{7} \mathrm{Nm}^{-2}$
(c) $10^{6} \mathrm{Nm}^{-2}$
(d) $10^{5} \mathrm{Nm}^{-2}$

Narayan Hari

Numerade Educator

Problem 46

Identical springs of steel and copper are equally stretched.
(a) Less work is done on copper spring.
(b) Less work is done on steel spring.
(c) Equal work is done on both the springs.
(d) Data is incomplete

Ajay Singhal

Numerade Educator

Problem 47

An elevator cable is to have a maximum stress of $7 \times 10 \mathrm{Nm}^{-2}$ to allow for appropriate safety factors. Its maximum upward acceleration is $1.5 \mathrm{~ms}^{-2}$. If the cable has to support the total weight of $2000 \mathrm{~kg}$ of a loaded elevator, the area of cross-section of the cable should be:
(a) $3.38 \mathrm{~cm}^{2}$
(b) $3.28 \mathrm{~cm}^{2}$
(c) $4.28 \mathrm{~cm}^{2}$
(d) $2.28 \mathrm{~cm}^{2}$

Narayan Hari

Numerade Educator

Problem 48

To break a wire, force of $10^{6} \mathrm{Nm}^{-2}$ is required. If the density of the material is $3 \times 10^{3} \mathrm{kgm}^{-3}$ then the length of the wire which will break by its own weight will be:
(a) $34 \mathrm{~m}$
(b) $30 \mathrm{~m}$
(c) $300 \mathrm{~m}$
(d) $3 \mathrm{~m}$

Narayan Hari

Numerade Educator

Problem 49

A rubber cord catapult has cross-sectional area $25 \mathrm{~mm}^{2}$ and initial length of rubber cord is $10 \mathrm{~cm}$ It is stretched to $5 \mathrm{~cm}$ and then released to project missile of mass 5 gm. Taking $Y_{\text {rubber }}=5 \times 10^{8} \mathrm{Nm}^{-2}$ Velocity of projected missile is:
(a) $20 \mathrm{~ms}^{-1}$
(b) $100 \mathrm{~ms}^{-1}$
(c) $250 \mathrm{~ms}^{-1}$
(d) $200 \mathrm{~ms}^{-1}$

Narayan Hari

Numerade Educator

Problem 50

The length of a metal is $l_{1}$ when the tension in it is $T_{1}$ and is $l_{2}$ when the tension is $T_{2}$. The original length of the wire is:
(a) $\frac{\ell_{1}+l_{2}}{2}$
(b) $\frac{\ell_{1} T_{2}+\ell_{2} T_{1}}{T_{1}+T_{2}}$
(c) $\frac{\ell_{1} T_{2}-\ell_{2} T_{1}}{T_{1}-T_{2}}$
(d) $\sqrt{T_{1} T_{2} \ell_{1} \ell_{2}}$

Ajay Singhal

Numerade Educator

Problem 51

Let $Y_{\mathrm{S}}$ and $Y_{\mathrm{A}}$ represent Young's modulus for steel and aluminium respectively. It is said that steel is more elastic than aluminium. Therefore, it follows that:(a) $\quad Y_{\mathrm{s}}=Y_{\mathrm{A}}$
(b) $Y_{\mathrm{s}}<Y_{\mathrm{A}}$
(c) $Y_{s}>Y_{A}$
(d) $\frac{Y_{\mathrm{s}}}{Y_{\mathrm{A}}}$

Narayan Hari

Numerade Educator

Problem 52

A light rod of length $2 \mathrm{~m}$ suspended from the ceiling horizontally by means of two vertical wires of equal length. A weight $\mathrm{W}$ is hung from a light rod as shown in figure. The rod hung by means of a steel wire of cross-sectional area $A_{1}=0.1 \mathrm{~cm}^{2}$ and brass wire of cross-sectional area $A_{2}=0.2 \mathrm{~cm}^{2}$. To have equal stress in both wires, $T_{1} / T_{2}=$ ?

Narayan Hari

Numerade Educator

Problem 53

A metallic rod breaks when strain produced is $0.2 \%$. The Young's modulus of the material of the rod is $7 \times 10^{9} \mathrm{Nm}^{-2}$. What should be its area of cross-section to support a load of $10^{4} \mathrm{~N} ?$
(a) $7.1 \times 10^{-8} \mathrm{~m}^{2}$
(b) $7.1 \times 10^{-6} \mathrm{~m}^{2}$
(c) $7.1 \times 10^{-4} \mathrm{~m}^{2}$
(d) $7.1 \times 10^{-2} \mathrm{~m}^{2}$

Narayan Hari

Numerade Educator

Problem 54

Two wires are made of the same material and have the same volume. However, first wire has cross-sectional area $A$ and second wire has cross-sectional area $5 A$. If the length of first wire increases by $\Delta l$ on applying force $f$, how much force is needed to stretch second wire by the same amount?
(a) $14 f$
(b) $6 f$
(c) $25 f$
(d) $9 f$

Narayan Hari

Numerade Educator

Problem 55

When forces are applied on a body such that it is still in static equilibrium, then the extent to which the body gets deformed, depends on:
(a) nature of the material
(b) magnitude of deforming force
(c) Both (a) and (b)
(d) None of these

Narayan Hari

Numerade Educator

Problem 56

following tour wires ot length $L$ and raduk are made of the same material. Which of these will have the largest extension, when the same tension is applied?
(a) $L=100 \mathrm{~cm}, r=0.2 \mathrm{~mm}$
(b) $L=200 \mathrm{~cm}, r=0.4 \mathrm{~mm}$
(c) $L=300 \mathrm{~cm}, r=0.6 \mathrm{~mm}$
(d) $L=400 \mathrm{~cm}, r=0.8 \mathrm{~mm}$

Ajay Singhal

Numerade Educator

Problem 57

A force of $6 \times 10^{6} \mathrm{Nm}^{-2}$ is required for breaking a material. Then density $\rho$ of the material is $3 \times 10^{3} \mathrm{kgm}^{-3}$. If the wire is to break under its own weight, the length of wire made of that material should be: (take $\mathrm{g}=10 \mathrm{~ms}^{-2}$ )
(a) $20 \mathrm{~m}$
(b) $200 \mathrm{~m}$
(c) $100 \mathrm{~m}$
(d) $2000 \mathrm{~m}$

Narayan Hari

Numerade Educator

Problem 72

The Young's modulus of a wire of length $L$ and radius $\mathrm{r}$ is $Y$. If the length is reduced to $L / 3$ and radius is, $R / 3$ then the Young's modulus will be:
(a) $Y$
(b) $Y / 3$
(c) $Y / 9$
(d) $Y / 27$

Narayan Hari

Numerade Educator

Problem 73

The Young's modulus of the material of a given wire can be determined by using:
(a) Voltmeter
(b) Searle's apparatus
(c) Sonometer
(d) Metre bridge

Narayan Hari

Numerade Educator

Problem 74

When a pressure of 300 atmosphere is applied on a spherical ball, then its volume reduces to $0.03 \% .$ The bulk modulus of the material is:
(a) $10^{11}$
(b) $10^{8}$
(c) $10^{6}$
(d) $10^{5}$

Narayan Hari

Numerade Educator

Problem 75

A uniform cube is subjected to volume compression. If each side is decreased by $2 \%$, then bulk strain is:
(a) $0.01$
(b) $0.02$
(c) $0.03$
(d) $0.06$

Narayan Hari

Numerade Educator

Problem 76

When a $5 \mathrm{~kg}$ mass is hung vertically on a light spring that obeys Hooke's law, the spring stretches by $1 \mathrm{~cm}$. The work required to be done by an external agent in stretching this spring by $5 \mathrm{~cm}$ will be: $\left(\mathrm{g}=9.8 \mathrm{msec}^{-2}\right)$
(a) $4.95 \mathrm{~J}$
(b) $6.125 \mathrm{~J}$
(c) $6.495 \mathrm{~J}$
(d) $6.245 \mathrm{~J}$

Narayan Hari

Numerade Educator

Problem 77

The modulus of rigidity is also known as:
(a) Bulk modulus
(b) Young's modulus
(c) Shear modulus
(d) Poisson's ratio

Narayan Hari

Numerade Educator

Problem 78

Which one of the following statements is incorrect? In the case of:(a) shearing stress there is no change in volume.
(b) hydraulic stress there is no change in shape.
(c) shearing stress there is change in shape.
(d) hydraulic stress there is no change in volume.

Narayan Hari

Numerade Educator

Problem 79

Two parallel and opposite forces each $4000 \mathrm{~N}$ are applied tangentially to the upper and lower faces of a cubical metal block of side $20 \mathrm{~cm} .$ The angle of shear is: (The shear modulus of the metal is $80 \mathrm{GPa}$.)
(a) $1.25 \times 10^{-4} \mathrm{rad}$
(b) $2.25 \times 10^{-6} \mathrm{rad}$
(c) $1.25 \times 10^{-6} \mathrm{rad}$
(d) $1.25 \times 10^{-5} \mathrm{rad}$

Narayan Hari

Numerade Educator

Problem 80

Consider four steel wires of dimensions given $(d=$ diameter and $l=$ length $):$(i) $1=1 \mathrm{~m}, \mathrm{~d}=2 \mathrm{~mm}$
(ii) $\mathrm{l}=1 \mathrm{~m}, \mathrm{~d}=4 \mathrm{~mm}$
(iii) $\mathrm{l}=1 \mathrm{~m}, \mathrm{~d}=3 \mathrm{~mm}$
(iv) $\mathrm{l}=1 \mathrm{~m}, \mathrm{~d}=1 \mathrm{~mm}$If same force is applied to all the wires then the elastic potential energy stored will be maximum in wire:
(a) (i)
(b) (ii)
(c) (iii)
(d) (iv)

Narayan Hari

Numerade Educator

Problem 81

If in a wire of Young's modulus $Y$, longitudinal strain $X$ is produced, then the value of potential energy stored in its unit volume will be:
(a) $2 Y X^{2}$
(b) $\frac{Y X^{2}}{2}$
(c) $\frac{Y^{2} X}{2}$
(d) $Y X^{2}$

Narayan Hari

Numerade Educator

Problem 82

The Poisson's ratio of a material is $0.5$. If a force is applied to a wire of this material, there is a decrease in the cross-sectional area by $6 \%$. The percentage increase in the length is:
(a) $11 \%$
(b) $12 \%$
(c) $3 \%$
(d) $6 \%$

Narayan Hari

Numerade Educator

Problem 83

The Young's modulus of the material of a wire is $2 \times 10^{10} \mathrm{Nm}^{-2}$. If the elongation strain is $2 \%$, then the energy stored in the wire per unit volume in $\mathrm{Jm}^{-3}$ is:
(a) $4 \times 10^{6}$
(b) $10^{6}$
(c) $2 \times 10^{6}$
(d) $8 \times 10^{6}$

Narayan Hari

Numerade Educator

Problem 84

A $7 \mathrm{~m}$ long wire is fixed to the ceiling. A weight of $12 \mathrm{~kg}$ is hung at the lower end and is $2 \mathrm{~m}$ above the floor. The wire was elongated by $2 \mathrm{~mm}$. The energy stored in the wire due to stretching is:
(a) Zero
(b) $0.05 \mathrm{~J}$
(c) $0.12 \mathrm{~J}$
(d) $1.2 \mathrm{~J}$

Narayan Hari

Numerade Educator

Problem 85

A wire suspended vertically from one of its ends is stretched by attaching a weight of $250 \mathrm{~N}$ to the lower end. The weight stretches the wire by $2 \mathrm{~mm}$. Then the elastic energy stored in the wire is:
(a) $0.25 \mathrm{~J}$
(b) $2.5 \mathrm{~J}$
(c) $25 \mathrm{~J}$
(d) $250 \mathrm{~J}$

Narayan Hari

Numerade Educator

Problem 86

For an ideal liquid
(a) bulk modulus is infinite and shear modulus is zero.
(b) bulk modulus is zero and shear modulus is infinite.
(c) bulk modulus is infinite and shear modulus is also infinite.
(d) bulk modulus is zero and shear modulus is also zero.

Kamlesh Goyal

Numerade Educator

Problem 87

Which of the following statements is correct?
(a) The bulk modulus for solids is much smaller than for liquids.
(b) Solid are least compressible.
(c) For a system in equilibrium, the value of bulk modulus is not always positive.
(d) The SI unit of bulk modulus is not same that of pressure.

Ajay Singhal

Numerade Educator

Problem 88

A sphere contracts in volume by $0.02 \%$, when taken to the bottom of sea $1 \mathrm{~km}$ deep. The bulk modulus of the material of the sphere is: (Given density of sea water may be taken as $1.0 \times 10^{3} \mathrm{kgm}^{-3}$ )
(a) $4.9 \times 10^{10} \mathrm{Nm}^{-2}$
(b) $4.9 \times 10^{8} \mathrm{Nm}^{-2}$
(c) $9.8 \times 10^{10} \mathrm{Nm}^{-2}$
(d) $9.8 \times 10^{8} \mathrm{Nm}^{-2}$

Ajay Singhal

Numerade Educator

Problem 89

The bulk modulus of water if its volume changes from $100 \mathrm{~L}$ to $99.5 \mathrm{~L}$ under a pressure of $100 \mathrm{~atm}$ is:
(Take one $\mathrm{atm}=10^{5} \mathrm{Nm}^{-2}$ )
(a) $2 \times 10^{9} \mathrm{Nm}^{-2}$
(b) $2 \times 10^{10} \mathrm{Nm}^{-2}$
(c) $2 \times 10^{8} \mathrm{Nm}^{-2}$
(d) $2 \times 10^{7} \mathrm{Nm}^{-2}$

Ajay Singhal

Numerade Educator

Problem 90

The bulk moduli of ethanol, mercury and water are given as $0.9,25$, and $2.2$ respectively in units of $10^{9} \mathrm{Nm}^{-2}$. For a given value of pressure, the fractional compression in volume is $\Delta V / V .$ Which of the following statements about $\Delta V / V$ for these three liquids is correct?
(a) Ethanol $<$ Water $<$ Mercury
(b) Water $>$ Ethanol $>$ Mercury
(c) Ethanol $>$ Water $>$ Mercury
(d) Ethanol $>$ Mercury $>$ Water

Ajay Singhal

Numerade Educator

Problem 91

A material has Poisson's ratio $0.60 .$ If a uniform roo of it suffers a longitudinal strain of $2 \times 10^{-3}$ then the percentage change in volume is:
(a) $4.4 \times 10^{-3}$
(b) $4 \times 10^{-3}$
(c) $2.2 \times 10^{-3}$
(d) $4.4 \times 10^{-4}$

Ajay Singhal

Numerade Educator

Problem 92

When a force is applied on a wire of uniform crosssection area $2 \times 10^{6} \mathrm{~m}^{-2}$ and length $6 \mathrm{~m}$, the increase in length is $1 \mathrm{~mm}$. Energy stored in it will be:
$\left(Y=2 \times 10^{11} \mathrm{Nm}^{-2}\right)$
(a) $0.033 \mathrm{~J}$
(b) $0.33 \mathrm{~J}$
(c) $0.023 \mathrm{~J}$
(d) $3.3 \mathrm{~J}$

Ajay Singhal

Numerade Educator

Problem 93

The relation between $Y, G$, and $B$ is:
(a) $\frac{2}{Y}=\frac{1}{3 G}+\frac{1}{9 B}$
(b) $\frac{9}{Y}=\frac{3}{G}+\frac{1}{B}$
(c) $\frac{1}{Y}=\frac{9}{G}+\frac{3}{B}$
(d) $\frac{9}{Y}=\frac{1}{G}+\frac{3}{B}$

Ajay Singhal

Numerade Educator

Problem 94

How much pressure should be applied on a litre of water if it is to be compressed by $0.3 \%$ ? (Bulk modulus of water $=2100 \mathrm{MPa}$ )
(a) $6300 \times 10^{3} P_{a}$
(b) $6300 \times 10^{5} \mathrm{P}_{a}$
(c) $6300 P_{a}$
(d) $630 \times 10^{5} P_{a}$

Ajay Singhal

Numerade Educator

Problem 95

The volume change of a solid copper cube $20 \mathrm{~cm}$ on an edge, when subjected to a pressure of $7 \mathrm{MPa}$ is:
(Bulk modulus of copper $=140 \mathrm{GPa}$ )
(a) $4 \times 10^{-7} \mathrm{~m}^{3}$
(b) $4 \times 10^{-6} \mathrm{~m}^{3}$
(c) $5 \times 10^{-7} \mathrm{~m}^{3}$
(d) $5 \times 10^{-6} \mathrm{~m}^{3}$

Ajay Singhal

Numerade Educator

Problem 96

For a given material, the Young's modulus is $2.4$ times that of the modulus of rigidity. Its Poisson's ratio is:
(a) $0.4$
(b) $0.3$
(c) $0.2$
(d) $0.5$

Ajay Singhal

Numerade Educator

Problem 97

Dimensional formula for modulus of rigidity is:
(a) $\left[\mathrm{M}^{1} \mathrm{~L}^{-1} \mathrm{~T}^{2}\right]$
(b) $\left[\mathrm{M}^{1} \mathrm{~L}^{1} \mathrm{~T}^{2}\right]$
(c) $\left[\mathrm{M}^{1} \mathrm{~L}^{-1} \mathrm{~T}^{-2}\right]$
(d) $\left[\mathrm{M}^{1} \mathrm{~L}^{-2} \mathrm{~T}^{-2}\right]$

Ajay Singhal

Numerade Educator

Problem 98

Liquids have no Poisson's ratio, because
(a) they have no definite shape.
(b) they have greater volume.
(c) they have lesser density than solid.
(d) they have definite shape.

Ajay Singhal

Numerade Educator

Problem 99

The theoretical value of Poisson's ratio lies between:
(a) $-1$ to $\frac{1}{2}$
(b) $-\frac{3}{4}$ to $-\frac{1}{2}$
(c) $-\frac{1}{2}$ to 1
(d) 1 to 2

Ajay Singhal

Numerade Educator

Problem 100

Match the pairs:$\mathrm{A}$ Work done in (i) $\frac{F L}{A x}$
stretching wireB Energy stored in (ii) $Y$ (strain) $^{2} / 2$ unit volume of wireC Modulus of rigidity (iii) $\frac{1}{2} \times$ stress $\times$ strain $\times$ volume(a) A-(ii), B-(i), C-(iii)
(c) A-(iii), B-(ii), C-(i)
(b) A-(ii), B-(iii), C-(i)
(d) A-(i), B-(iii), C-(ii)

Ajay Singhal

Numerade Educator