Objective NCERT at your FINGERTIPS: Physics

NCERT

Chapter 9

Mechanical Properties of Solids - all with Video Answers

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Chapter Questions

Problem 1

Solids which break above the clastic limit are called
(a) brittle
(b) ductile
(c) malleable
(d) elastic

Kamlesh Goyal

Kamlesh Goyal

Numerade Educator

Problem 2

Out of the following the most plastic material is
(a) iron
(b) wood
(c) rubber
(d) plasticine

Kamlesh Goyal

Numerade Educator

Problem 3

Match the Column I with Column II.
$$
\begin{array}{|l|l|l|l|}
\hline {\text { Column I }} & {\text { Column II }} \\
\hline \text { (A) } & \begin{array}{l}
\text { A body which regains its } \\
\text { original shape after the removal } \\
\text { of external forces. }
\end{array} & \text { (p) } \text { Elasticity } \\
\hline \text { (B) } & \begin{array}{l}
\text { A body which does not regain its } \\
\text { original shape after the removal } \\
\text { of external forces. }
\end{array} & \text { (q) } & \text { Elastic } \\
\hline \text { (C) } & \begin{array}{l}
\text { A body which does not show } \\
\text { any deformation on applying } \\
\text { external forces. }
\end{array} & \text { (r) } & \text { Plastic } \\
\text { (D) } & \text { The property of the body to } & \text { (s) } & \text { Rigid } \\
& \text { regain its original configuration } & \text { body } \\
& \begin{array}{l}
\text { when the deforming forces are } \\
\text { removed }
\end{array} & & \\
\hline
\end{array}
$$
(a) $A-q, B-r, C-s, D-p$
(b) $A-p, B-q, C-r, D-s$
(c) $A-r, B-s, C-p, D-q$
(d) $A-s, B-p, C-q, D=r$

Akshaya Rs

Numerade Educator

Problem 4

The substance which shows practically no elastic after effect is
(a) copper
(b) silver
(c) rubber
(d) quartz

Kamlesh Goyal

Numerade Educator

Problem 5

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) data is insufficient.

Kamlesh Goyal

Numerade Educator

Problem 6

The potential energy $U$ of two atoms of a diatomic molecule as a function of distance $r$ between the atoms as shown in the given figure.
Read the following statements carefully.
1. The equilibrium separation distance between the atoms is equal to $r_{2}$.
2. At $r=r_{1}$, the force between the atom is repulsive.
3. For $r>r_{2}$, the force between the atoms is attractive, Which of the above statements is true?
(a) 1 only
(b) 2 only
(c) 3 only
(d) 2 and 3

Akshaya Rs

Numerade Educator

Problem 7

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.

Aman Kumar

Numerade Educator

Problem 8

Shear stress is related to
(a) length
(b) area
(c) volume
(d) shape

Kamlesh Goyal

Numerade Educator

Problem 9

If the volume of a wire remains constant when subjected to tensile stress, the value of Poisson's ratio of the material of the wire is
(a) $0.1$
(b) $0.2$
(c) $0.4$
(d) $0.5$

Kamlesh Goyal

Numerade Educator

Problem 10

Fluids can develop
(a) longitudinal strain only longitudinal and shearing strain
(b) longitudinal, and shearing and volumetric strain
(c) volumetric strain only
(d) volumetric strain only

Aman Kumar

Numerade Educator

Problem 11

Which of the following following statements is correct regarding Poisson's ratio?
(a) It is the ratio of the longitudinal strain to the lateral strain. value is independent of the nature of the
(b) IIts value is independent of the nature of the material.
(c) It is unitless and dimensionless quantity.
(d) The practical value of Poisson's ratio lies between 0 and 1 .

Aman Kumar

Numerade Educator

Problem 12

If two equal and opposite deforming forces are applied parallel to the crosssectional area of the cylinder as shown in the figure, there is a relative displacement the opposite faces $F$ between of the cylinder. The ratio of $\Delta x$ to $L$ is known as
(a) longitudinal strain
(b) volumetric strain
(c) shearing strain
(d) Poisson's ratio

Aman Kumar

Numerade Educator

Problem 13

Stress is a _________ quantity.
(a) scalar
(b) vector
(c) tensor
(d) dimensionless

Kamlesh Goyal

Numerade Educator

Problem 14

The breaking stress of a wire depends upon
(a) length of the wire
(b) radius of the wire
(c) material of the wire
(d) shape of the cross-section

Kamlesh Goyal

Numerade Educator

Problem 15

A wire is suspended from the ceiling and stretched under the action of a weight $F$ 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 $\frac{F}{A}$.
(b) Tensile stress at any cross section is zero.
(c) Tensile stress at any cross section $A$ of the wire is $\frac{2 F}{A}$
(d) Tension at any cross section $A$ of the wire is $2 F$.

Aman Kumar

Numerade Educator

Problem 16

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

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Problem 17

According to Hooke's law of elasticity, if stress is increased, the ratio of stress to strain
(a) decreases
(b) increases
(c) becomes zero
(d) remains constant

Kamlesh Goyal

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?

Aman Kumar

Numerade Educator

Problem 19

Substances which can be stretched to cause large strains are called
(a) isomers
(b) plastomers
(c) elastomers
(d) polymers

Kamlesh Goyal

Numerade Educator

Problem 20

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 21

Figure shows the strain-stress curve for a given material. The Young's modulus of the material is
(a) $5 \times 10^{9} \mathrm{~N} \mathrm{~m}^{-2}$
(b) $5 \times 10^{10} \mathrm{~N} \mathrm{~m}^{-2}$
(c) $7.5 \times 10^{9} \mathrm{~N} \mathrm{~m}^{-2}$
(d) $7.5 \times 10^{10} \mathrm{~N} \mathrm{~m}^{-2}$

Aman Kumar

Numerade Educator

Problem 22

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) $O A, C, D$
(b) $O B, D, E$
(c) $O A, D, E$
(d) $O B, C, D$

Aman Kumar

Numerade Educator

Problem 23

Which of the following graphs represents stressstrain variation for elastomers?

Aman Kumar

Numerade Educator

Problem 24

The ratio of tensile stress to the longitudinal strain is defined as
(a) bulk modulus
(b) Young's modulus
(c) shear modulus
(d) compressibility

Kamlesh Goyal

Numerade Educator

Problem 25

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 26

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 27

Identical springs of steel and copper $\left(Y_{\text {steel }}>Y_{\text {copper }}\right)$ 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.

Kamlesh Goyal

Numerade Educator

Problem 28

Let $Y_{S}$ and $Y_{A}$ represent Young's modulus for steel and aluminium respectively. It is said that steel is more elastic than aluminium. Therefore, it follows that
(a) $Y_{5}=Y_{A}$
(b) $Y_{S}<Y_{A}$
(c) $Y_{S}>Y_{A}$
(d) $\underline{Y}_{s}$

Kamlesh Goyal

Numerade Educator

Problem 29

Which of the following substances has highes of Young's modulus?
(a) Aluminium
(b) Iron
(c) Copper
(d) Steel

Kamlesh Goyal

Numerade Educator

Problem 30

If the work done in stretching a wire by $1 \mathrm{~m}_{\mathrm{m}}$ $2 \mathrm{~J}$, the work necessary for stretching another with of same material but with double radius of $\mathrm{cr}_{\mathrm{O}}$ s, section and half the length by $1 \mathrm{~mm}$ is
(a) $16 \mathrm{~J}$
(b) $8 \mathrm{~J}$
(c) $4 \mathrm{~J}$
(d) $\frac{1}{4} j$

Akshaya Rs

Numerade Educator

Problem 31

The following four wires of length $L$ and radius, are made of the same material. Which of these will have the largest extension, when the same tension 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) $L=400 \mathrm{~cm}, r=0.8 \mathrm{~mm}$

Kamlesh Goyal

Numerade Educator

Problem 32

Four identical hollow cylindrical columns, support big structure of mass $M$. The inner and outer radii of a column are $R_{1}$ and $R_{2}$ respectively. Assuming the load distribution to be uniform, the compressional strain of each column is (where $Y$ is Young's modulus of the column)
(a) $\frac{M g}{\pi\left(R_{2}^{2}-R_{1}^{2}\right) Y}$
(b) $\frac{M g}{4 \pi\left(R_{2}^{2}-R_{1}^{2}\right) Y}$
(c) $\frac{M g}{\pi\left(R_{1}^{2}-R_{2}^{2}\right) Y}$
(d) $\frac{M g}{4 \pi\left(R_{1}^{2}-R_{2}^{2}\right) Y}$

Aman Kumar

Numerade Educator

Problem 33

The elastic energy stored per unit volume in a stretched wire is
(a) $\frac{1}{2} \frac{\text { stress }}{Y}$
(b) $\frac{1}{2} \frac{(\text { stress })^{2}}{Y}$
(c) $\frac{1}{2} \frac{(\text { stress })^{2}}{Y^{2}}$
(d) $\frac{1}{2} \frac{\text { stress }}{Y^{2}}$

Kamlesh Goyal

Numerade Educator

Problem 34

Two wires of the same material and length but diameter in the ratio $1: 2$ are stretched by the same load. The ratio of elastic potential energy per unit volume for the two wires is
(a) $1: 1$
(b) $2: 1$
(c) $4: 1$
(d) $16: 1$

Kamlesh Goyal

Numerade Educator

Problem 35

Young's modulus of a wire depends on
(a) diameter of the wire
(b) mass hanging from the wire
(c) length of the wire
(d) material of the wire

Kamlesh Goyal

Numerade Educator

Problem 36

light rod of length $2 \mathrm{~m}$ is suspended from the ceiling holleoth tied to its ends. One of the wires is of equal length and is of cross-section $0.1 \mathrm{~cm}^{2}$ and made of steel arass of cross-section $0.2 \mathrm{~cm}^{2}$. Along the other of the rod at what distance a weight may be hung to produce equal stresses in both the wires?
$\left(Y_{\text {Sucel }}=2 \times 10^{11} \mathrm{~N} \mathrm{~m}^{-2}, Y_{\text {Brass }}=1 \times 10^{11} \mathrm{~N} \mathrm{~m}^{-2}\right.$ )
(a) $\frac{4}{3} \mathrm{~m}$ from steel wire
(b) $\frac{4}{3} \mathrm{~m}$ from brass wire
(c) $1 \mathrm{~m}$ from steel wire
(d) $\frac{1}{4} \mathrm{~m}$ from brass wire

Akshaya Rs

Numerade Educator

Problem 37

In the question number 36, at which distance a In the quert be hung along the rod, in order to weight may produce equal strains in both the wires?
(a) $\frac{4}{3} \mathrm{~m}$ from steel wire
(b) $\frac{4}{3} \mathrm{~m}$ from brass wire
(c) $1 \mathrm{~m}$ from steel wire
(d) $\frac{1}{4} \mathrm{~m}$ from brass wire

Akshaya Rs

Numerade Educator

Problem 38

A wire of length $L$ and radius $r$ is clamped at one end. On stretching the other end of the wire with a force $F$, the increase in its length is $l$. If another wire of same material but of length $2 L$ and radius $2 r$ is stretched with a force $2 F$, the increase in its length will be
(a) $\frac{l}{4}$
(b) $\frac{l}{2}$
(c) $l$
(d) $2 l$

Kamlesh Goyal

Numerade Educator

Problem 39

The radii and Young's moduli of two uniform wires $A$ and $B$ are in the ratio $2: 1$ and $1: 2$ respectively. Both wires are subjected to the same longitudinal force. If the increase in length of the wire $A$ is one percent, the percentage increase in length of the wire $B$ is
(a) $1.0$
(b) $1.5$
(c) $2.0$
(d) $3.0$

Kamlesh Goyal

Numerade Educator

Problem 40

A steel cable with a radius $2 \mathrm{~cm}$ supports a chairlift at a ski area. If the maximum stress is not to exceed $10^{8} \mathrm{~N} \mathrm{~m}^{-2}$, the maximum load the cable can support is
(a) $4 \pi \times 10^{5} \mathrm{~N}$
(b) $4 \pi \times 10^{4} \mathrm{~N}$
(c) $2 \pi \times 10^{5} \mathrm{~N}$
(d) $2 \pi \times 10^{4} \mathrm{~N}$

Kamlesh Goyal

Numerade Educator

Problem 41

A steel rod of length $1 \mathrm{~m}$ and radius $10 \mathrm{~mm}$ is stretched by a force $100 \mathrm{kN}$ along its length. The stress produced in the rod is $\left(Y_{\text {Steel }}=2 \times 10^{11} \mathrm{~N} \mathrm{~m}^{-2}\right.$ )
(a) $3.18 \times 10^{6} \mathrm{~N} \mathrm{~m}^{-2}$
(b) $3.18 \times 10^{7} \mathrm{~N} \mathrm{~m}^{-2}$
(c) $3.18 \times 10^{8} \mathrm{~N} \mathrm{~m}^{-2}$
(d) $3.18 \times 10^{9} \mathrm{~N} \mathrm{~m}^{-2}$.

Kamlesh Goyal

Numerade Educator

Problem 42

In the question number 41, the percentage strain produced in the rod is
(a) $0.04 \%$
(b) $0.08 \%$
(c) $0.16 \%$
(d) $0.24 \%$

Kamlesh Goyal

Numerade Educator

Problem 43

A steel wire can support a maximum load of $\mathrm{W}$ before reaching its elastic limit. How much load can another wire, made out of identical steel, but with a radius one half the radius of the first wire, support before reaching its elastic limit?
(a) $\mathrm{W}$
(b) $\frac{\mathrm{W}}{2}$
(c) $\frac{\mathrm{W}}{\mathrm{4}}$
(d) $4 \mathrm{~W}$

Kamlesh Goyal

Numerade Educator

Problem 44

A uniform rod of mass $m$, length $L$, area of cross- section $A$ is rotated about an axis passing through one of its ends and perpendicular to its length with constant angular velocity $\omega$ in a horizontal plane. If $Y$ is the Young's modulus of the material of rod, the increase in its length due to rotation of rod is
(a) $\frac{m \omega^{2} L^{2}}{A Y}$
(b) $\frac{m \omega^{2} L^{2}}{2 A Y}$
(c) $\frac{m \omega^{2} L^{2}}{3 A Y}$
(d) $\frac{2 m \omega^{2} L^{2}}{A Y}$

Akshaya Rs

Numerade Educator

Problem 45

A wire stretches by a certain amount under a load. If the load and radius both are increased to four times. The stretch caused in the wire is
(a) $l$
(b) $\frac{l}{2}$
(c) $\frac{1}{3}$
(d) $\frac{l}{4}$

Kamlesh Goyal

Numerade Educator

Problem 46

A wire of length $L$ has a linear mass density $\mu$ and area of cross-section $A$ and the Young's modulus $Y$ is suspended vertically from a rigid support. The extension produced in the wire due to its own weight is
(a) $\frac{\mu g L^{2}}{Y A}$
(b) $\frac{\mu g L^{2}}{2 Y A}$
(c) $\frac{2 \mu g L^{2}}{Y A}$
(d) $\frac{2 \mu g L^{2}}{3 Y A}$

Kamlesh Goyal

Numerade Educator

Problem 47

In the question number 46 , if the mass $M$ is hung at the free end of the wire, then the extension produced in the wire is
(a) $\frac{\mu g L^{2}+M g L}{2 Y A}$
(b) $\frac{2 \mu g L^{2}+M g L}{2 Y A}$
(c) $\frac{\mu g L^{2}+2 M g L}{2 Y A}$
(d) $\frac{\mu g L^{2}+M g L}{Y A}$

Akshaya Rs

Numerade Educator

Problem 48

A $15 \mathrm{~kg}$ mass fastened to the end of a steel wire of unstretched length $1.0 \mathrm{~m}$ is whirled in a vertical circle with an angular velocity of 2 rev $\mathrm{s}^{-1}$ at the bottom of the circle. The cross-section of the wire is $0.05 \mathrm{~cm}^{2}$. The elongation of the wire when the mass is at the lowest point of its path is (Take, $g=10 \mathrm{~m} \mathrm{~s}^{-2}, \mathrm{Y}_{\text {stecl }}=2 \times 10^{11} \mathrm{~N} \mathrm{~m}^{-2}$ )
(a) $0.52 \mathrm{~mm}$
(b) $1.52 \mathrm{~mm}$
(c) $2.52 \mathrm{~mm}$
(d) $3.52 \mathrm{~mm}$

Akshaya Rs

Numerade Educator

Problem 49

A wire of length $L$ and area of cross-section $A$, is stretched by a load. The elongation produced in the wire is $\angle$ If $Y$ is the Young's modulus of the naterial of the wire, then the force constant of the wire is
(a) $\frac{Y Z}{A}$
(b) $\frac{Y}{A}$
(c) $\frac{Y A}{L}$
(d) $\frac{Y A}{l}$

Kamlesh Goyal

Numerade Educator

Problem 50

A metal wire of length $L_{1}$ and area of cross-section $A$ is attached to a rigid support. Another metal wire of length $L$, and of the same cross-sectional area is athached to the free end of the first wire. A body of mass $M$ is then suspended from the free end of the second wire. If $Y_{1}$ and $Y_{2}^{\prime}$ are the Young's moduli of the wires respectively, the effective force constant of the system of two wires is
(a) $\frac{\left[\left(Y_{1} Y_{2}\right) .4\right]}{\left[2\left(Y_{1} L_{2}+Y_{2} L_{1}\right)\right]}$
(b) $\frac{\left[\left(Y_{1} Y_{2}\right) A\right]}{\left(L_{1} L_{2}\right)^{1 / 2}}$
(c) $\frac{\left[\left(Y_{1} Y_{2}\right) A\right]}{\left(Y_{1} L_{2}+Y_{2} L_{1}\right)}$
(d) $\frac{\left[\left(Y_{1} Y_{2}\right)^{1 / 2} A\right]}{\left(L_{1} L_{2}\right)^{L^{2}}}$

Akshaya Rs

Numerade Educator

Problem 51

The area of a cross-section of steel wire is $0.1 \mathrm{~cm}^{2}$ and Young's modulus of steel is $2 \times 10^{11} \mathrm{~N} \mathrm{~m}^{-2}$. The force required to stretch by $0.1 \%$ of its length is
(a) $\frac{\left[\left(Y_{1} Y_{2}\right) A\right]}{\left[2\left(Y_{1} L_{2}+Y_{2} L_{1}\right)\right]}$
(b) $\frac{\left[\left(Y_{1} Y_{2}\right) A\right]}{\left(L_{1} L_{2}\right)^{1 / 2}}$
(c) $4000 \mathrm{~N}$
(d) $5000 \mathrm{~N}$

Akshaya Rs

Numerade Educator

Problem 52

A stone of mass $m$ tied to one end of a wire of length $L$ The diameter of the wire is $D$ and it is suspended vertically. The stone is now rotated in a horizontal plane and makes an angle $\theta$ with the vertical. If Young's modulus of the wire is $Y$, then the increase in the length of the wire is
(a) $\frac{4 m g L}{-D^{2} Y}$
(b) $\frac{4 m g L}{\pi D^{2} Y \sin \theta}$
(c) $\frac{4 m g L}{\pi D^{2} Y \cos \theta}$
(d) $\frac{4 m g L}{\pi D^{2} Y \tan \theta}$

Akshaya Rs

Numerade Educator

Problem 53

When the load on a wire is increased from $3 \mathrm{~kg}$ wt to $5 \mathrm{~kg}$ wt the elongation increases from $0.61 \mathrm{~mm}$ to $1.02 \mathrm{~mm}$. The required work done during the extension of the wire is
(a) $16 \times 10^{-3} \mathrm{~J}$
(b) $8 \times 10^{-2} \mathrm{~J}$
(c) $20 \times 10^{-2} \mathrm{~J}$
(d) $11 \times 10^{-3} \mathrm{~J}$

Kamlesh Goyal

Numerade Educator

Problem 54

If the ratio of diameters, lengths and Young's moduli of steel and brass wires shown in the figure are $p$, $q$ and $r$ respectively. Then the corresponding ratio of increase in their lengths would be
(a) $\frac{3 q}{5 p^{2} r}$
(b) $\frac{5 q}{3 p^{2} r}$
(c) $\frac{3 q}{5 p r}$
(d) $\frac{5 q}{3 p r}$

Akshaya Rs

Numerade Educator

Problem 55

A copper wire of length $2.4 \mathrm{~m}$ and a steel wire of $1.6 \mathrm{~m}$, both of diameter $3 \mathrm{~mm}$, are connected end. When stretched by a load, the net elongatiod found to be $0.7 \mathrm{~mm}$. The load applied is $\left(Y_{\text {cumer }}=1.2 \times 10^{11} \mathrm{Nm}^{-2}, Y_{\text {seel }}=2 \times 10^{11} \mathrm{~N}\right.$
(a) $1.2 \times 10^{2} \mathrm{~N}$
(b) $1.8 \times 10^{2} \mathrm{~N}$
(c) $2.4 \times 10^{2} \mathrm{~N}$
(d) $3.2 \times 10^{2} \mathrm{~N}$

Akshaya Rs

Numerade Educator

Problem 56

In the question number 55 , the ratio of elony steel to the copper wires is
(a) $\frac{5}{2}$
(b) $\frac{2}{5}$
(c) $\frac{3}{2}$
(d) $\frac{2}{3}$

Khoobchandra Agrawal

Khoobchandra Agrawal

Numerade Educator

Problem 57

A steel wre of rengul 4.s $\mathrm{m}$ and cross-sectiong area $3 \times 10^{-5} \mathrm{~m}^{2}$ stretches by the same amount $\mathrm{ks}_{2}$ copper wire of length $3.5 \mathrm{~m}$ and cross-sectional $a_{4}$ of $4 \times 10^{-5} \mathrm{~m}^{2}$ under a given load. The ratio of the Young's modulus of steel to that of copper is
(a) $1.3$
(b) $1.5$
(c) $1.7$
(d) $1.9$

Akshaya Rs

Numerade Educator

Problem 58

The Young's modulus of a wire of length $L$ and $r a d$ is $r$ is $Y$. If the length is reduced to $\frac{L}{2}$ and radius is $\frac{r}{2}$ then the Young's modulus will be
(a) $\frac{Y}{2}$
(b) $Y$
(c) $2 Y$
(d) $4 Y$

Kamlesh Goyal

Numerade Educator

Problem 59

A copper and a steel wire of the same diameter 2te connectedend toend A deforming force Fisappliedto this composite wire which causes a total elongation of $1 \mathrm{~cm}$. The two wires will have
(a) the same stress and strain
(b) the same stress but different strain
(c) the same strain but different stress
(d) different strains and stress

Aman Kumar

Numerade Educator

Problem 60

Which of the following apparatus is used to determine the Young's modulus of the material of given wire?
(a) Searle
(b) sonometer
(c) Metre bridge
(d) Resonance tube

Kamlesh Goyal

Numerade Educator

Problem 61

With rise in temperature, the Young's modulus of elasticity
(a) increases
(b) decreases
(c) remains unchanged
(d) None of these

Kamlesh Goyal

Numerade Educator

Problem 62

The length of a rubber cord is $l_{1} \mathrm{~m}$ when the tension is $4 \mathrm{~N}$ and $l_{2} \mathrm{~m}$ when the tension is $6 \mathrm{~N}$. The length when the tension is $9 \mathrm{~N}$, is
(a) $\left(2.5 l_{2}-1.5 l_{1}\right) \mathrm{m}$
(b) $\left(6 l_{2}-1.5 l_{1}\right) \mathrm{m}$
(c) $\left(3 l_{1}-2 l_{2}\right) \mathrm{m}$
(d) $\left(3.5 l_{2}-2.5 l_{1}\right) \mathrm{m}$

Kamlesh Goyal

Numerade Educator

Problem 63

The ratio of shearing stress to the shearing strain is defined as
(a) Young's modulus
(b) bulk modulus
(c) shear modulus
(d) compressibility

Kamlesh Goyal

Numerade Educator

Problem 64

The Shear modulus is also known as
(a) bulk modulus
(b) Young's modulus
(c) modulus of rigidity
(d) Possion's ratio

Kamlesh Goyal

Numerade Educator

Problem 65

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

Aman Kumar

Numerade Educator

Problem 66

A bar cross-sectional area $A$ is subjected two equal and opposite tensile forces at its ends as shown in figure. Consider a plane $B B^{\prime}$ making an angle $\theta$ with the length.
The ratio of tensile stress to the shearing stress on
the plane $B B^{\prime}$ is
(a) $\tan \theta$
(b) $\sec \theta$
(c) $\cot \theta$
(d) $\cos \theta$

Akshaya Rs

Numerade Educator

Problem 67

In the question number 66, for what value of $\theta$, shearing stress is maximum?
(a) $0^{\circ}$
(b) $30^{\circ}$
(c) $45^{\circ}$
(d) $90^{\circ}$

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Problem 68

Two parallel and opposite forces each $5000 \mathrm{~N}$ are applied tangentially to the upper and lower faces of a cubical metal block of side $25 \mathrm{~cm}$. The angle of shear is (The shear modulus of the metal is $80 \mathrm{GPa}$.)
(a) $10^{-4} \mathrm{rad}$
(b) $10^{-5} \mathrm{rad}$
(c) $10^{-6} \mathrm{rad}$
(d) $10^{-7} \mathrm{rad}$

Akshaya Rs

Numerade Educator

Problem 69

The edge of an aluminium cube is $10 \mathrm{~cm}$ long. One face of the cube is firmly fixed to a vertical wall. A mass of $100 \mathrm{~kg}$ is then attached to the opposite face of the cube. The vertical deflection of this face is (Shear modulus of aluminium $=25 \mathrm{GPa}, g=10 \mathrm{~m} \mathrm{~s}^{-2}$ ).
(a) $4 \times 10^{-5} \mathrm{~m}$
(b) $4 \times 10^{-6} \mathrm{~m}$
(c) $4 \times 10^{-7} \mathrm{~m}$
(d) $4 \times 10^{-8} \mathrm{~m}$

Akshaya Rs

Numerade Educator

Problem 70

For most materials the Young's modulus is $n$ times the modulus of rigidity, where $n$ is
(a) 2
(b) 3
(c) 4
(d) 5

Kamlesh Goyal

Numerade Educator

Problem 71

A square lead slab of side $50 \mathrm{~cm}$ and thickness $10 \mathrm{~cm}$ is subjected to a shearing force (on its narrow face) of $9 \times 10^{4} \mathrm{~N}$. The lower edge is riveted to the floor. How much will the upper edge be displaced? (Shear modulus of lead $=5.6 \times 10^{9} \mathrm{~N} \mathrm{~m}^{-2}$ )
(a) $0.16 \mathrm{~mm}$
(b) $1.6 \mathrm{~mm}$
(c) $0.16 \mathrm{~cm}$
(d) $1.6 \mathrm{~cm}$

Akshaya Rs

Numerade Educator

Problem 72

The metal cube of side $10 \mathrm{~cm}$ is subjected to a shearing stress of $10^{4} \mathrm{~N} \mathrm{~m}^{-2}$. The modulus of rigidity if the top of the cube is displaced by $0.05 \mathrm{~cm}$ with respect to its bottom is
(a) $2 \times 10^{6} \mathrm{~N} \mathrm{~m}^{-2}$
(b) $10^{5} \mathrm{~N} \mathrm{~m}^{-2}$
(c) $1 \times 10^{7} \mathrm{~N} \mathrm{~m}^{-2}$
(d) $4 \times 10^{5} \mathrm{~N} \mathrm{~m}^{-2}$
73. For an ide

Akshaya Rs

Numerade Educator

Problem 73

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 74

Which of the following statements is incorrect?
(a) The bulk modulus for solids is much larger than for liquids.
(b) Gases are least compressible.
(c) For a system in equilibrium, the value of bulk modulus is always positive.
(d) The SI unit of bulk modulus is same that of pressure.

Aman Kumar

Numerade Educator

Problem 75

A sphere contracts in volume by $0.01 \%$, 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 $1.0 \times 10^{3} \mathrm{~kg} \mathrm{~m}^{-3}$ ).
(a) $4.9 \times 10^{10} \mathrm{~N} \mathrm{~m}^{-2}$
(b) $9.8 \times 10^{10} \mathrm{~N} \mathrm{~m}^{-2}$
(c) $4.9 \times 10^{9} \mathrm{~N} \mathrm{~m}^{-2}$
(d) $9.8 \times 10^{9} \mathrm{~N} \mathrm{~m}^{-2}$

Aman Kumar

Numerade Educator

Problem 76

The bulk modulus of water if its volume changes from 100 litre to $99.5$ litre under a pressure of $100 \mathrm{~atm}$ is
(Take $1 \mathrm{~atm}=10^{5} \mathrm{~N} \mathrm{~m}^{-2}$ )
(a) $2 \times 10^{7} \mathrm{~N} \mathrm{~m}^{-2}$
(b) $2 \times 10^{8} \mathrm{~N} \mathrm{~m}^{-2}$
(c) $2 \times 10^{9} \mathrm{~N} \mathrm{~m}^{-2}$
(d) $2 \times 10^{10} \mathrm{~N} \mathrm{~m}^{-2}$

Kamlesh Goyal

Numerade Educator

Problem 77

The average depth of Indian ocean is about $3000 \mathrm{~m}$. The fractional compression, $\frac{\Delta V}{V}$ of water at the bottom of the ocean is (Given : Bulk modulus of the water $=2.2 \times 10^{9} \mathrm{~N} \mathrm{~m}^{-2}$ and $\left.g=10 \mathrm{~m} \mathrm{~s}^{-2}\right)$
(a) $0.82 \%$
(b) $0.91 \%$
(c) $1.36 \%$
(d) $1.24 \%$

Aman Kumar

Numerade Educator

Problem 78

The density of water at the surface of the ocean is $\rho$ and atmospheric pressure is $\mathrm{P}_{0}$. If the bulk modulus of water is $K$, what is the density of ocean water at a depth where the pressure is $n P_{0} ?$
(a) $\frac{\rho K}{K-n P_{0}}$
(b) $\frac{\rho K}{K+n P_{0}}$
(c) $\frac{\rho K}{K-(n-1) P_{0}}$
(d) $\frac{\rho K}{K+(n-1) P_{0}}$

Aman Kumar

Numerade Educator

Problem 79

If stress-strain relation for volumetric change is in the form $\frac{\Delta V}{V_{0}}=K P$ where $P$ is applied uniform pressure, then $K$ stands for
(a) shear modulus
(b) compressibility
(c) Young's modulus
(d) bulk modulus

Kamlesh Goyal

Numerade Educator

Problem 80

Among solids, liquids and gases, which posses the greatest bulk modulus?
(a) Solids
(b) Liquids
(c) Gases
(d) Both solids and liquids

Kamlesh Goyal

Numerade Educator

Problem 81

A glass slab is subjected to a pressure of $10 \mathrm{~atm}$. The fractional change in its volume is (Bulk modulus of glass $=37 \times 10^{9} \mathrm{~N} \mathrm{~m}^{-2}$ $\left.1 \mathrm{~atm}=1 \times 10^{5} \mathrm{~N} \mathrm{~m}^{-2}\right)$
(a) $2.7 \times 10^{-2}$
(b) $2.7 \times 10^{-3}$
(c) $2.7 \times 10^{-4}$
(d) $2.7 \times 10^{-5}$

Aman Kumar

Numerade Educator

Problem 82

To what depth must a rubber ball be taken in deep sea so that its volume is decreased by $0.1 \% .$ (Take, density of sea water $=10^{3} \mathrm{~kg} \mathrm{~m}^{-3}$, bulk modulus of rubber $\left.=9 \times 10^{8} \mathrm{~N} \mathrm{~m}^{-2}, g=10 \mathrm{~m} \mathrm{~s}^{-2}\right)$
(a) $9 \mathrm{~m}$
(b) $18 \mathrm{~m}$
(c) $90 \mathrm{~m}$
(d) $180 \mathrm{~m}$

Aman Kumar

Numerade Educator

Problem 83

The compressibility of water is $6 \times 10^{-10} \mathrm{~N}^{-1} \mathrm{~m}^{2}$. If one litre is subjected to a pressure of $4 \times 10^{7} \mathrm{~N} \mathrm{~m}^{-2}$, the decrease in its volume is
(a) $10 \mathrm{cc}$
(b) $24 \mathrm{cc}$
(c) $15 \mathrm{cc}$
(d) $12 \mathrm{cc}$

Kamlesh Goyal

Numerade Educator

Problem 84

How much pressure should be applied on a litre of water if it is to be compressed by $0.1 \%$ ? (Bulk modulus of water $=2100 \mathrm{MPa}$ )
(a) $2100 \mathrm{kPa}$
(b) $210 \mathrm{kPa}$
(c) $2100 \mathrm{MPa}$
(d) $210 \mathrm{MPa}$

Kamlesh Goyal

Numerade Educator

Problem 85

The volume change of a solid copper cube $10 \mathrm{~cm}$ on an edge, when subjected to a pressure of $7 \mathrm{MPa}$ is (Bulk modulus of copper $=140 \mathrm{GPa}$ )
(a) $5 \times 10^{-2} \mathrm{~cm}^{3}$
(b) $10 \times 10^{-2} \mathrm{~cm}^{3}$
(c) $15 \times 10^{-2} \mathrm{~cm}^{3}$
(d) $20 \times 10^{-2} \mathrm{~cm}^{3}$

Aman Kumar

Numerade Educator

Problem 86

A metal cylinder of length $L$ is subjected to a uniform compressive force $F$ as shown in the figure. The material of the cylinder has Young's modulus $Y$ and Poisson's ratio \sigma. The change in volume of the cylinder is
(a) $\frac{\sigma F L}{Y}$
(b) $\frac{(1-\sigma) F L}{Y}$
(c) $\frac{(1+2 \sigma) F L}{Y}$
(d) $\frac{(1-2 \sigma) F L}{Y}$

Akshaya Rs

Numerade Educator

Problem 87

For a given material, the Young's modulus is 2.4. times that of the modulus of rigidity. Its poisson's ratio is
(a) $2.4$
(b) $1.2$
(c) $0.4$
(d) $0.2$

Aman Kumar

Numerade Educator

Problem 88

A material has Poisson's ratio $0.5$. 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) $2 e_{t_{0}}$

Kamlesh Goyal

Numerade Educator

Problem 89

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

Akshaya Rs

Numerade Educator

Problem 90

A material has Poisson's ratio 0.2. If a uniform $r_{0 d}$ of its suffers longitudinal strain $4.0 \times 10^{-3}$, cal $_{\text {culate }} t h_{t}$ percentage change in its volume.
(a) $0.15 \%$
(b) $0.02 \%$
(c) $0.24 \%$
(d) $0.48 \%$

Akshaya Rs

Numerade Educator

Problem 91

One end of a nylon rope of length $4.5 \mathrm{~m}$ and diamete $6 \mathrm{~mm}$ is fixed to a free limb. A monkey weighing $100 \mathrm{~N}$ jumps to catch the free end and stays there Find the elongation of the rope (Given $Y_{04 n g^{\prime}}$ modulus of nylon $=4.8 \times 10^{11} \mathrm{~N} \mathrm{~m}^{-2}$ and $\mathrm{P}_{\text {oiss }_{0} n^{\prime} \text { s }}$ ratio of nylon $=0.2$.)
(a) $0.332 \mu \mathrm{m}$
(b) $0.151 \mu \mathrm{m}$
(c) $0.625 \mu \mathrm{m}$
(d) $0.425 \mu \mathrm{m}$

Akshaya Rs

Numerade Educator

Problem 92

In question number 91 , what will be the change in the diameter of the rope?
(a) $8.8 \times 10^{-9} \mathrm{~m}$
(b) $7.4 \times 10^{-9} \mathrm{~m}$
(c) $6.4 \times 10^{-8} \mathrm{~m}$
(d) $5.6 \times 10^{-9} \mathrm{~m}$

Akshaya Rs

Numerade Educator

Problem 93

Assuming that shear stress at the base of a mountain is equal to the force per unit area due to its weight. Calculate the maximum possible height of $a$ mountain on the earth if breaking stress of a typical rock is $3 \times 10^{8} \mathrm{~N} \mathrm{~m}^{-2}$ and its density is $3 \times 10^{3} \mathrm{~kg} \mathrm{~m}^{-3}$.
(Take $g=10 \mathrm{~m} \mathrm{~s}^{-2}$ )
(a) $4 \mathrm{~km}$
(b) $8 \mathrm{~km}$
(c) $10 \mathrm{~km}$
(d) $16 \mathrm{~km}$

Akshaya Rs

Numerade Educator

Problem 94

With what minimum acceleration can a fireman slide down a rope whose breaking strength is two third of his weight?
(a) $\frac{g}{2}$
(b) $\frac{2}{3} g$
(c) $\frac{3}{2} g$
(d) $\frac{g}{3}$

Kamlesh Goyal

Numerade Educator

Problem 95

A beam of metal supported at the two ends is loaded at the centre. The depression at the centre is proportional to
(a) $Y^{2}$
(b) $Y$
(c) $\frac{1}{Y}$
(d) $\frac{1}{y^{2}}$

Kamlesh Goyal

Numerade Educator

Problem 96

Two Strips of metal are riveted together at their end by four rivets, each of diameter $6 \mathrm{~mm}$. Assume that each rivet is to carry one quarter of the load. If the shearing stress on the rivet is not to exceed $6.9 \times 10^{7} \mathrm{~Pa}$ the maximum tension that can be exerted by the riveted strip is
(a) $2 \times 10^{3} \mathrm{~N}$
(b) $3.9 \times 10^{3} \mathrm{~N}$
(c) $7.8 \times 10^{5} \mathrm{~N}$
(d) $15.6 \times 10^{3} \mathrm{~N}$

Akshaya Rs

Numerade Educator

Problem 97

A spring is made of steel and not of copper because
(a) steel is more elastic than copper
(b) steel is less elastic than copper
(c) steel is more plastic than copper
(d) steel is less plastic than copper

Kamlesh Goyal

Numerade Educator

Problem 98

A bar of length $I$ breadth $b$ and depth $d$ is supported, At its ends and is loaded at the centre by a load $W$. If $y$ is the Young's modulus of the material of the bar, then the depression $\delta$ at the centre is
(a) $\frac{W l^{3}}{4 b d^{3} Y}$
(b) $\frac{W b^{3}}{4 d l^{3} Y}$
(c) $\frac{w d^{3}}{4 l b^{3} Y}$
(d) $\frac{W l^{3}}{b d^{3} Y}$

Kamlesh Goyal

Numerade Educator

Problem 99

Two rods $A$ and $B$ of the same material and length have radii $r_{1}$ and $r_{2}$ respectively. When they are rigidly fixed at one end and twisted by the same torque applied at the other end, the ratio
$$\left[\begin{array}{l}\text { the angle of twist at the end of } A \\ \text { the angle of twist at the end of } B\end{array}\right]$$
(a) $\frac{r_{1}^{2}}{r_{2}^{2}}$
(b) $\frac{r_{1}^{3}}{r_{2}^{3}}$
(c) $\frac{r_{2}^{4}}{r_{1}^{4}}$
(d) $\frac{r_{1}^{4}}{r_{2}^{4}}$

Supratim Pal

Numerade Educator

Problem 100

Match the Column I with Column II.
$$
\begin{array}{|l|l|l|l|}
\hline {\text { Column I }} & && {\text { Column II }} \\
\hline \text { (A) } & \begin{array}{l}
\text { The shape of rubber heel } \\
\text { changes under stress }
\end{array} & \text { (p) } & \begin{array}{l}
\text { Young's } \\
\text { modulus of } \\
\text { elasticity is } \\
\text { involved }
\end{array} \\
\hline \text { (B) } & \begin{array}{l}
\text { In a suspended bridge, } \\
\text { there is a strain in the } \\
\text { ropes by the load of the } \\
\text { bridge }
\end{array} & \text { (q) } & \begin{array}{l}
\text { Bulk modulus } \\
\text { of elasticity is } \\
\text { involved }
\end{array} \\
\hline \text { (C) } & \begin{array}{l}
\text { In an automobile tyre, } \\
\text { when air is compressed, } \\
\text { the shape of tyre changes }
\end{array} & \text { (r) } & \begin{array}{l}
\text { Modulus of } \\
\text { rigidity is } \\
\text { involved }
\end{array} \\
\hline \text { (D) } & \begin{array}{l}
\text { A solid body is subjected } \\
\text { to a deforming force }
\end{array} & \text { (s) } & \begin{array}{l}
\text { All the moduli } \\
\text { of elasticity } \\
\text { are involved }
\end{array} \\
\hline
\end{array}
$$
(a) $\mathrm{A}-\mathrm{q}, \mathrm{B}-\mathrm{r}, \mathrm{C}-\mathrm{s}, \mathrm{D}-\mathrm{p}$
(b) $\mathrm{A}-\mathrm{p}, \mathrm{B}-\mathrm{q}, \mathrm{C}-\mathrm{r}, \mathrm{D}-\mathrm{s}$
(c) $\mathrm{A}-\mathrm{r}, \mathrm{B}-\mathrm{q}, \mathrm{C}-\mathrm{p}, \mathrm{D}-\mathrm{s}$
(d) $A-r, B-p, C-q, D-s$

Prem Bijarniya

Numerade Educator