Elasticity Test 2

Total Questions:50 Total Time: 60 Min

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Questions 1 of 50

Question:When a certain weight is suspended from a long uniform wire, its length increases by one cm. If the same weight is suspended from another wire of the same material and length but having a diameter half of the first one then the increase in length will be

Answers Choices:

0.5 cm

2 cm

4 cm

8 cm

Questions 2 of 50

Question:Hook's law defines

Answers Choices:

Stress

Strain

Modulus of elasticity

Elastic limit

Questions 3 of 50

Question:A wire is loaded by 6 kg at its one end, the increase in length is 12 mm. If the radius of the wire is doubled and all other magnitudes are unchanged, then increase in length will be

Answers Choices:

6 mm

3 mm

24 mm

48 mm

Questions 4 of 50

Question:The area of cross-section of a wire of length 1.1 metre is 1 mm2. It is loaded with 1 kg. If Young's modulus of copper is \(1.1 \times {10^{11}}\,N/{m^2}\), then the increase in length will be (If \(g = 10\,m/{s^2})\)

Answers Choices:

0.01 mm

0.075 mm

0.1 mm

0. 15 mm

Questions 5 of 50

Question:A and B are two wires. The radius of A is twice that of B. They are stretched by the some load. Then the stress on B is

Answers Choices:

Equal to that on A

Four times that on A

Two times that on A

Half that on A

Questions 6 of 50

Question:If the length of a wire is reduced to half, then it can hold the ......... load

Answers Choices:

Half

Same

Double

One fourth

Questions 7 of 50

Question:To double the length of a iron wire having \(0.5\,c{m^2}\) area of cross-section, the required force will be \((Y = {10^{12}}\,dyne/c{m^2})\)

Answers Choices:

\(1.0 \times {10^{ - 7}}N\)

\(1.0 \times {10^7}N\)

\(0.5 \times {10^{ - 7}}N\)

\(0.5 \times {10^{12}}\)dyne

Questions 8 of 50

Question:The spring balance does not read properly after its long use, because

Answers Choices:

The elasticity of spring increases

The elasticity decreases

Its plastic power decreases

Its plastic power increases

Questions 9 of 50

Question: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

Answers Choices:

Four times for wire A as for wire B

Twice for wire A as for wire B

Half for wire A as for wire B

One-fourth for wire A as for wire B

Questions 10 of 50

Question:Longitudinal stress of \(1\,kg/m{m^2}\) is applied on a wire. The percentage increase in length is \((Y = {10^{11}}\,N/{m^2})\)

Answers Choices:

0

0

0

0.01

Questions 11 of 50

Question:A steel wire is stretched with a definite load. If the Young's modulus of the wire is Y. For decreasing the value of Y

Answers Choices:

Radius is to be decreased

Radius is to be increased

Length is to be increased

None of the above

Questions 12 of 50

Question:The interatomic distance for a metal is \(3 \times {10^{ - 10}}\,m\). If the interatomic force constant is \(3.6 \times {10^{ - 9}}\,N/{\AA}\), then the Young's modulus in \(N/{m^2}\) will be

Answers Choices:

\(1.2 \times {10^{11}}\)

\(4.2 \times {10^{11}}\)

\(10.8 \times {10^{ - 19}}\)

\(2.4 \times {10^{10}}\)

Questions 13 of 50

Question:Two identical wires of rubber and iron are stretched by the same weight, then the number of atoms in the iron wire will be

Answers Choices:

Equal to that of rubber

Less than that of the rubber

More than that of the rubber

None of the above

Questions 14 of 50

Question:The force constant of a wire does not depend on

Answers Choices:

Nature of the material

Radius of the wire

Length of the wire

None of the above

Questions 15 of 50

Question:The elastic limit for a gas

Answers Choices:

Exists

Exists only at absolute zero

Exists for a perfect gas

Does not exist

Questions 16 of 50

Question:If Young's modulus for a material is zero, then the state of material should be

Answers Choices:

Solid

Solid but powder

Gas

None of the above

Questions 17 of 50

Question:Liquids have no Poisson's ratio, because

Answers Choices:

It has no definite shape

It has greater volume

It has lesser density than solid

None of the above

Questions 18 of 50

Question:A wire of length L and radius r is rigidly fixed 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 2L and radius 2r is stretched with a force of 2F, the increase in its length will be

Answers Choices:

l

2l

\(\frac{l}{2}\)

\(\frac{l}{4}\)

Questions 19 of 50

Question:Density of rubber is d. A thick rubber cord of length L and cross-section area A undergoes elongation under its own weight on suspending it. This elongation is proportional to

Answers Choices:

Dl

Ad/L

\(Ad/{L^2}\)

\(d{L^2}\)

Questions 20 of 50

Question:The ratio of two specific heats of gas \({C_p}/{C_v}\) for argon is 1.6 and for hydrogen is 1.4. Adiabatic elasticity of argon at pressure P is E. Adiabatic elasticity of hydrogen will also be equal to E at the pressure

Answers Choices:

P

\(\frac{8}{7}P\)

\(\frac{7}{8}P\)

1.4 P

Questions 21 of 50

Question:The relation between \(\gamma ,\,\eta \) and K for a elastic material is

Answers Choices:

\(\frac{1}{\eta } = \frac{1}{{3\gamma }} + \frac{1}{{9K}}\)

\(\frac{1}{K} = \frac{1}{{3\gamma }} + \frac{1}{{9\eta }}\)

\(\frac{1}{\gamma } = \frac{1}{{3K}} + \frac{1}{{9\eta }}\)

\(\frac{1}{\gamma } = \frac{1}{{3\eta }} + \frac{1}{{9K}}\)

Questions 22 of 50

Question:A fixed volume of iron is drawn into a wire of length L. The extension x produced in this wire by a constant force F is proportional to

Answers Choices:

\(\frac{1}{{{L^2}}}\)

\(\frac{1}{L}\)

\({L^2}\)

L

Questions 23 of 50

Question:In solids, inter-atomic forces are

Answers Choices:

Totally repulsive

Totally attractive

Combination of (1) and (2)

None of these

Questions 24 of 50

Question:A force F is applied on the wire of radius r and length L and change in the length of wire is l. If the same force F is applied on the wire of the same material and radius 2r and length 2L, Then the change in length of the other wire is

Answers Choices:

l

2l

l/2

4l

Questions 25 of 50

Question:The modulus of elasticity is dimensionally equivalent to

Answers Choices:

Surface tension

Stress

Strain

None of these

Questions 26 of 50

Question:Under elastic limit the stress is

Answers Choices:

Inversely, proportional to strain

Directly proportional to strain

Square root of strain

Independent of strain

Questions 27 of 50

Question:A copper wire of length 4.0m and area of cross-section \(1.2\,c{m^2}\) is stretched with a force of \(4.8 \times {10^3}\) N. If Young’s modulus for copper is \(1.2 \times {10^{11}}\,N/{m^2},\) the increase in the length of the wire will be

Answers Choices:

1.33 mm

1.33 cm

2.66 mm

2.66 cm

Questions 28 of 50

Question:A metal bar of length L and area of cross-section A is clamped between two rigid supports. For the material of the rod, its Young’s modulus is Y and coefficient of linear expansion is \(\alpha \). If the temperature of the rod is increased by \(\Delta {t^o}C,\) the force exerted by the rod on the supports is

Answers Choices:

\(Y\,A\,L\,\Delta t\)

\(Y\;A\;\alpha \,\Delta t\)

\(\frac{{YL\alpha \Delta t}}{A}\)

\(Y\alpha \,A\,L\,\Delta t\)

Questions 29 of 50

Question:According to Hook’s law of elasticity, if stress is increased, the ratio of stress to strain

Answers Choices:

Increases

Decreases

Becomes zero

Remains constant

Questions 30 of 50

Question:A pan with set of weights is attached with a light spring. When disturbed, the mass-spring system oscillates with a time period of 0.6 s. When some additional weights are added then time period is 0.7s. The extension caused by the additional weights is approximately given by

Answers Choices:

1.38 cm

3.5 cm

1.75 cm

2.45 cm

Questions 31 of 50

Question:A wire of cross section 4 mm\(^2\) is stretched by 0.1 mm by a certain weight. How far (length) will be wire of same material and length but of area 8 mm\(^2\) stretch under the action of same force

Answers Choices:

0.05 mm

0.10 mm

0.15 mm

0.20 mm

0.25 mm

Questions 32 of 50

Question:A substance breaks down by a stress of 10\(^6\) N/m\(^2\). If the density of the material of the wire is 3×10\(^3\) kg/m\(^3\), then the length of the wire of the substance which will break under its own weight when suspended vertically, is

Answers Choices:

66.6 m

60.0 m

33.3 m

30.0 m

Questions 33 of 50

Question:A rubber cord 10 m long is suspended vertically. How much does it stretch under its own weight (Density of rubber is 1500 kg/m\(^{\rm{3}}\), Y = 5×10\(^8\) N/m\(^2\), g = 10 m/s\(^2\))

Answers Choices:

15×10­\(^{ - 4}\) m

7.5×10­\(^{ - 4}\) m

12×10­\(^{ - 4}\) m

25×10­\(^{ - 4}\) m

Questions 34 of 50

Question:The value of Poisson's ratio lies between

Answers Choices:

1 to \(\frac{1}{2}\)

\( - \frac{3}{4}\) to \( - \frac{1}{2}\)

\( - \frac{1}{2}\) to 1

1 to 2

Questions 35 of 50

Question:The compressibility of a material is

Answers Choices:

Product of volume and its pressure

The change in pressure per unit change in volume strain

The fractional change in volume per unit change in pressure

None of the above

Questions 36 of 50

Question:When a pressure of 100 atmosphere is applied on a spherical ball, then its volume reduces to 0.01%. The bulk modulus of the material of the rubber in \(dyne/c{m^2}\) is

Answers Choices:

\(10 \times {10^{12}}\)

\(100 \times {10^{12}}\)

\(1 \times {10^{12}}\)

\(20 \times {10^{12}}\)

Questions 37 of 50

Question:In the three states of matter, the elastic coefficient can be

Answers Choices:

Young's modulus

Coefficient of volume elasticity

Modulus of rigidity

Poisson's ratio

Questions 38 of 50

Question:Bulk modulus was first defined by

Answers Choices:

Young

Bulk

Maxwell

None of the above

Questions 39 of 50

Question:Which of the following relations is true

Answers Choices:

\(3Y = K(1 - \sigma )\)

\(K = \frac{{9\eta Y}}{{Y + \eta }}\)

\(\sigma = (6K + \eta )Y\)

\(\sigma = \frac{{0.5Y - \eta }}{\eta }\)

Questions 40 of 50

Question:Two wires A and B of same length and of the same material have the respective radii \({r_1}\) and \({r_2}\). Their one end is fixed with a rigid support, and at the other end equal twisting couple is applied. Then the ratio of the angle of twist at the end of A and the angle of twist at the end of B will be

Answers Choices:

\(\frac{{r_1^2}}{{r_2^2}}\)

\(\frac{{r_2^2}}{{r_1^2}}\)

\(\frac{{r_2^4}}{{r_1^4}}\)

\(\frac{{r_1^4}}{{r_2^4}}\)

Questions 41 of 50

Question:When a spiral spring is stretched by suspending a load on it, the strain produced is called

Answers Choices:

Shearing

Longitudinal

Volume

Transverse

Questions 42 of 50

Question:The Young's modulus of the material of a wire is \(6 \times {10^{12}}\,N/{m^2}\) and there is no transverse strain in it, then its modulus of rigidity will be

Answers Choices:

\(3 \times {10^{12}}\,N/{m^2}\)

\(2 \times {10^{12}}\,N/{m^2}\)

\({10^{12}}\,N/{m^2}\)

None of the above

Questions 43 of 50

Question:The work done in stretching an elastic wire per unit volume is or strain energy in a stretched string is

Answers Choices:

Stress \( \times \) Strain

\(\frac{1}{2} \times \)Stress \( \times \)Strain

\(2 \times {\rm{strain}} \times {\rm{stress}}\)

Stress/Strain

Questions 44 of 50

Question:Calculate the work done, if a wire is loaded by 'Mg' weight and the increase in length is 'l'

Answers Choices:

Mgl

Zero

Mgl/2

2Mgl

Questions 45 of 50

Question:Two wires of same diameter of the same material having the length l and 2l. If the force F is applied on each, the ratio of the work done in the two wires will be

Answers Choices:

01:02

01:04

02:01

01:01

Questions 46 of 50

Question:A 5 metre long wire is fixed to the ceiling. A weight of 10 kg is hung at the lower end and is 1 metre above the floor. The wire was elongated by 1 mm. The energy stored in the wire due to stretching is

Answers Choices:

Zero

0.05 joule

100 joule

500 joule

Questions 47 of 50

Question:On stretching a wire, the elastic energy stored per unit volume is

Answers Choices:

\(Fl/2AL\)

\(FA/2L\)

\(FL/2A\)

\(FL/2\)

Questions 48 of 50

Question:When a force is applied on a wire of uniform cross-sectional area \(3 \times {10^{ - 6}}\,{m^2}\)and length 4m, the increase in length is 1 mm. Energy stored in it will be \((Y = 2 \times {10^{11}}\,N/{m^2})\)

Answers Choices:

6250 J

0.177 J

0.075 J

0.150 J

Questions 49 of 50

Question:K is the force constant of a spring. The work done in increasing its extension from \({l_1}\) to \({l_2}\) will be

Answers Choices:

\(K({l_2} - {l_1})\)

\(\frac{K}{2}({l_2} + {l_1})\)

\(K(l_2^2 - l_1^2)\)

\(\frac{K}{2}(l_2^2 - l_1^2)\)

Questions 50 of 50

Question:When a 4 kg mass is hung vertically on a light spring that obeys Hooke's law, the spring stretches by 2 cms. The work required to be done by an external agent in stretching this spring by 5 cms will be \((g = 9.8\,metres/sex{c^2})\)

Answers Choices:

4.900 joule

2.450 joule

0.495 joule

0.245 joule