Elasticity Test 3

Total Questions:50 Total Time: 60 Min

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Questions 1 of 50

Question:On increasing the length by 0.5 mm in a steel wire of length 2 m and area of cross-section \(2\,m{m^2}\), the force required is [Y for steel\( = 2.2 \times {10^{11}}\,N/{m^2}]\)]

Answers Choices:

\(1.1 \times {10^5}\,N\)

\(1.1 \times {10^4}\,N\)

\(1.1 \times {10^3}\,N\)

\(1.1 \times {10^2}\,N\)

Questions 2 of 50

Question:If Young's modulus of iron is \(2 \times {10^{11}}\,N/{m^2}\) and the interatomic spacing between two molecules is \(3 \times {10^{ - 10}}\)metre, the interatomic force constant is

Answers Choices:

60 N/m

120 N/m

30 N/m

180 N/m

Questions 3 of 50

Question:In CGS system, the Young's modulus of a steel wire is \(2 \times {10^{12}}\). To double the length of a wire of unit cross-section area, the force required is

Answers Choices:

\(4 \times {10^6}\)Dynes

\(2 \times {10^{12}}\)dynes

\(2 \times {10^{12}}\)newtons

\(2 \times {10^8}\)dynes

Questions 4 of 50

Question:The material which practically does not show elastic after effect is

Answers Choices:

Copper

Rubber

Steel

Quartz

Questions 5 of 50

Question:Why the spring is made up of steel in comparison of copper

Answers Choices:

Copper is more costly than steel

Copper is more elastic than steel

Steel is more elastic than copper

None of the above

Questions 6 of 50

Question:Steel and copper wires of same length are stretched by the same weight one after the other. Young's modulus of steel and copper are \(2 \times {10^{11}}\,N/{m^2}\) and \(1.2 \times {10^{11}}\,N/{m^2}\). The ratio of increase in length

Answers Choices:

\(\frac{2}{5}\)

\(\frac{3}{5}\)

\(\frac{5}{4}\)

\(\frac{5}{2}\)

Questions 7 of 50

Question:An area of cross-section of rubber string is \(2\,c{m^2}\). Its length is doubled when stretched with a linear force of \(2 \times {10^5}\)dynes. The Young's modulus of the rubber in \(dyne/c{m^2}\) will be

Answers Choices:

\(4 \times {10^5}\)

\(1 \times {10^5}\)

\(2 \times {10^5}\)

\(1 \times {10^4}\)

Questions 8 of 50

Question:Increase in length of a wire is 1 mm when suspended by a weight. If the same weight is suspended on a wire of double its length and double its radius, the increase in length will be

Answers Choices:

2 mm

0.5 mm

4 mm

0.25 mm

Questions 9 of 50

Question:The elasticity of invar

Answers Choices:

Increases with temperature rise

Decreases with temperature rise

Does not depend on temperature

None of the above

Questions 10 of 50

Question:After effects of elasticity are maximum for

Answers Choices:

Glass

Quartz

Rubber

Metal

Questions 11 of 50

Question:In suspended type moving coil galvanometer, quartz suspension is used because

Answers Choices:

It is good conductor of electricity

Elastic after effects are negligible

Young's modulus is greater

There is no elastic limit

Questions 12 of 50

Question:A force of 200 N is applied at one end of a wire of length 2 m and having area of cross-section \({10^{ - 2}}\,c{m^2}\). The other end of the wire is rigidly fixed. If coefficient of linear expansion of the wire \(\alpha = 8 \times {10^{ - 6}}/^\circ C\) and Young's modulus \(Y = 2.2 \times {10^{11}}\,N/{m^2}\) and its temperature is increased by 5°C, then the increase in the tension of the wire will be

Answers Choices:

4.2 N

4.4 N

2.4 N

8.8 N

Questions 13 of 50

Question:In steel, the Young's modulus and the strain at the breaking point are \(2 \times {10^{11}}\,N{m^{ - 2}}\) and 0.15 respectively. The stress at the breaking point for steel is therefore

Answers Choices:

\(1.33 \times {10^{11}}\,N{m^{ - 2}}\)

\(1.33 \times {10^{12}}\,N{m^{ - 2}}\)

\(7.5 \times {10^{ - 13}}\,N{m^{ - 2}}\)

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

Questions 14 of 50

Question:Which of the following statements is correct

Answers Choices:

Hooke's law is applicable only within elastic limit

The adiabatic and isothermal elastic constants of a gas are equal

Young's modulus is dimensionless

Stress multiplied by strain is equal to the stored energy

Questions 15 of 50

Question:The force required to stretch a steel wire of \(1\,c{m^2}\) cross-section to 1.1 times its length would be \((Y = 2 \times {10^{11}}\,N{m^{ - 2}})\)

Answers Choices:

\(2 \times {10^6}\,N\)

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

\(2 \times {10^{ - 6}}N\)

\(2 \times {10^{ - 7}}\,N\)

Questions 16 of 50

Question:Which one of the following substances possesses the highest elasticity

Answers Choices:

Rubber

Glass

Steel

Copper

Questions 17 of 50

Question:Which one of the following quantities does not have the unit of force per unit area

Answers Choices:

Stress

Strain

Young's modulus of elasticity

Pressure

Questions 18 of 50

Question:A wire of cross-sectional area \(3\,m{m^2}\) is first stretched between two fixed points at a temperature of \(20^\circ C\). Determine the tension when the temperature falls to \(10^\circ C\). Coefficient of linear expansion \(\alpha = {10^{ - 5}}^\circ {C^{ - 1}}\) and \(Y = 2 \times {10^{11}}\,N/{m^2}\)

Answers Choices:

20 N

30 N

60 N

120 N

Questions 19 of 50

Question:To keep constant time, watches are fitted with balance wheel made of

Answers Choices:

Invar

Stainless steel

Tungsten

Platinum

Questions 20 of 50

Question:A wire is stretched by 0.01 m by a certain force F. Another wire of same material whose diameter and length are double to the original wire is stretched by the same force. Then its elongation will be

Answers Choices:

0.005 m

0.01 m

0.02 m

0.002 m

Questions 21 of 50

Question:The possible value of Poisson's ratio is

Answers Choices:

1

0.9

0.8

0.4

Questions 22 of 50

Question:The coefficient of linear expansion of brass and steel are \({\alpha _1}\) and \({\alpha _2}\). If we take a brass rod of length \({l_1}\) and steel rod of length \({l_2}\) at 0°C, their difference in length \(({l_2} - {l_1})\) will remain the same at a temperature if

Answers Choices:

\({\alpha _1}{l_2} = {\alpha _2}{l_1}\)

\({\alpha _1}l_2^2 = {\alpha _2}l_1^2\)

\(\alpha _1^2{l_1} = \alpha _2^2{l_2}\)

\({\alpha _1}{l_1} = {\alpha _2}{l_2}\)

Questions 23 of 50

Question:A steel wire of lm long and \(1\,m{m^2}\) cross section area is hang from rigid end. When weight of 1kg is hung from it then change in length will be (given \(Y = 2 \times {10^{11}}N/{m^2})\)

Answers Choices:

0.5 mm

0.25 mm

0.05 mm

5 mm

Questions 24 of 50

Question:A load W produces an extension of 1mm in a thread of radius r. Now if the load is made 4W and radius is made 2r all other things remaining same, the extension will become

Answers Choices:

4 mm

16 mm

1 mm

0.25 mm

Questions 25 of 50

Question:The units of Young ‘s modulus of elasticity are

Answers Choices:

\(N{m^{ - 1}}\)

N-m

\(N{m^{ - 2}}\)

\(N{\rm{ - }}{m^2}\)

Questions 26 of 50

Question:Two similar wires under the same load yield elongation of 0.1 mm and 0.05 mm respectively. If the area of cross- section of the first wire is \(4m{m^2},\) then the area of cross section of the second wire is

Answers Choices:

\(6m{m^2}\)

\(8m{m^2}\)

\(10\,m{m^2}\)

\(12\,m{m^2}\)

Questions 27 of 50

Question:A uniform plank of Young’s modulus Y is moved over a smooth horizontal surface by a constant horizontal force F. The area of cross section of the plank is A. The compressive strain on the plank in the direction of the force is

Answers Choices:

\(F/AY\)

\(2F/AY\)

\(\frac{1}{2}(F/AY)\)

\(3F/AY\)

Questions 28 of 50

Question:The mean distance between the atoms of iron is \(3 \times {10^{ - 10}}m\) and interatomic force constant for iron is \(7\,N\,/m\)The Young’s modulus of elasticity for iron is

Answers Choices:

\(2.33 \times {10^5}\,N/{m^2}\)

\(23.3 \times {10^{10}}\,N/{m^2}\)

\(233 \times {10^{10}}\,N/{m^2}\)

\(2.33 \times {10^{10}}\,N/{m^2}\)

Questions 29 of 50

Question:Two wires A and B are of same materials. Their lengths are in the ratio 1 : 2 and diameters are in the ratio 2 : 1 when stretched by force \({F_A}\) and \({F_B}\) respectively they get equal increase in their lengths. Then the ratio \({F_A}/{F_B}\) should be

Answers Choices:

1:2

1:1

2:1

8:1

Questions 30 of 50

Question:The breaking stress of a wire depends upon

Answers Choices:

Length of the wire

Radius of the wire

Material of the wire

Shape of the cross section

Questions 31 of 50

Question:The Poisson's ratio cannot have the value

Answers Choices:

0.7

0.2

0.1

0.5

Questions 32 of 50

Question:There is no change in the volume of a wire due to change in its length on stretching. The Poisson's ratio of the material of the wire is

Answers Choices:

0.5

0.50

0.25

0.25

Questions 33 of 50

Question: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

Answers Choices:

0.6

0.4

0.2

Zero

Questions 34 of 50

Question:Four identical rods are stretched by same force. Maximum extension is produced in

Answers Choices:

\(L = 10cm,\,\,D = 1\,mm\)

\(L = 100\,cm,\,D = \,2mm\)

\(L = 200\,cm,\,D = \,3mm\)

\(L = 300\,cm,\,D = \,4\,mm\)

Questions 35 of 50

Question:A uniform cube is subjected to volume compression. If each side is decreased by 1%, then bulk strain is

Answers Choices:

0.01

0.06

0.02

0.03

Questions 36 of 50

Question:A ball falling in a lake of depth 200 m shows 0.1% decrease in its volume at the bottom. What is the bulk modulus of the material of the ball

Answers Choices:

\(19.6 \times {10^8}\,N/{m^2}\)

\(19.6 \times {10^{ - 10}}\,N/{m^2}\)

\(19.6 \times {10^{10}}\,N/{m^2}\)

\(19.6 \times {10^{ - 8}}\,N/{m^2}\)

Questions 37 of 50

Question:The isothermal bulk modulus of a gas at atmospheric pressure is

Answers Choices:

\(1\,mm\)of Hg

\(13.6\,mm\)of Hg

\(1.013 \times {10^5}\,N/{m^2}\)

\(2.026 \times {10^5}N/{m^2}\)

Questions 38 of 50

Question:Coefficient of isothermal elasticity \({E_\theta }\) and coefficient of adiabatic elasticity \({E_\varphi }\)are related by\((\gamma = {C_p}/{C_v})\)

Answers Choices:

\({E_\theta } = \gamma \,{E_\varphi }\)

\({E_\varphi } = \gamma \,{E_\theta }\)

\({E_\theta } = \gamma /{E_\varphi }\)

\({E_\theta } = {\gamma ^2}{E_\varphi }\)

Questions 39 of 50

Question:If the Young's modulus of the material is 3 times its modulus of rigidity, then its volume elasticity will be

Answers Choices:

Zero

Infinity

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

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

Questions 40 of 50

Question:Modulus of rigidity of a liquid

Answers Choices:

Non zero constant

Infinite

Zero

Can not be predicted

Questions 41 of 50

Question:For a given material, the Young's modulus is 2.4 times that of rigidity modulus. Its Poisson's ratio is

Answers Choices:

2.4

1.2

0.4

0.2

Questions 42 of 50

Question:A cube of aluminium of sides 0.1 m is subjected to a shearing force of 100 N. The top face of the cube is displaced through 0.02 cm with respect to the bottom face. The shearing strain would be

Answers Choices:

0.02

0.1

0.01

0

Questions 43 of 50

Question:If the force constant of a wire is K, the work done in increasing the length of the wire by l is

Answers Choices:

Kl/2

Kl

\(K{l^2}/2\)

\(K{l^2}\)

Questions 44 of 50

Question:If the tension on a wire is removed at once, then

Answers Choices:

It will break

Its temperature will reduce

There will be no change in its temperature

Its temperature increases

Questions 45 of 50

Question:When strain is produced in a body within elastic limit, its internal energy

Answers Choices:

Remains constant

Decreases

Increases

None of the above

Questions 46 of 50

Question:When shearing force is applied on a body, then the elastic potential energy is stored in it. On removing the force, this energy

Answers Choices:

Converts into kinetic energy

Converts into heat energy

Remains as potential energy

None of the above

Questions 47 of 50

Question:A wire of length L and cross-sectional area A is made of a material of Young's modulus Y. It is stretched by an amount x. The work done is

Answers Choices:

\(\frac{{YxA}}{{2L}}\)

\(\frac{{Y{x^2}A}}{L}\)

\(\frac{{Y{x^2}A}}{{2L}}\)

\(\frac{{2Y{x^2}A}}{L}\)

Questions 48 of 50

Question:The elastic energy stored in a wire of Young's modulus Y is

Answers Choices:

\(Y \times \frac{{{\rm{Strai}}{{\rm{n}}^{\rm{2}}}}}{{{\rm{Volume}}}}\)

Stress \( \times \) Strain \( \times \) Volume

\(\frac{{{\rm{Stres}}{{\rm{s}}^{\rm{2}}} \times {\rm{Volume}}}}{{2Y}}\)

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

Questions 49 of 50

Question:A wire of length 50 cm and cross sectional area of 1 sq. mm is extended by 1 mm. The required work will be \((Y = 2 \times {10^{10}}\,N{m^{ - 2}})\)

Answers Choices:

\(6 \times {10^{ - 2}}\,J\)

\(4 \times {10^{ - 2}}\,J\)

\(2 \times {10^{ - 2}}\,J\)

\(1 \times {10^{ - 2}}\,J\)

Questions 50 of 50

Question:The work per unit volume to stretch the length by 1% of a wire with cross sectional area of \(1\,m{m^2}\) will be. \([Y = 9 \times {10^{11}}\,N/{m^2}]\)

Answers Choices:

\(9 \times {10^{11}}\,J\)

\(4.5 \times {10^7}\,J\)

\(9 \times {10^7}J\)

\(4.5 \times {10^{11}}\,J\)