# Elasticity Test 1

Total Questions:50 Total Time: 60 Min

Remaining:

## Questions 1 of 50

Question:The increase in length is l of a wire of length L by the longitudinal stress. Then the stress is proportional to

L/l

l/L

$$l \times L$$

$${l^2} \times L$$

## Questions 2 of 50

Question:The dimensions of four wires of the same material are given below. In which wire the increase in length will be maximum when the same tension is applied

Length 100 cm, Diameter 1 mm

Length 200 cm, Diameter 2 mm

Length 300 cm, Diameter 3 mm

Length 50 cm, Diameter 0.5 mm

## Questions 3 of 50

Question:The ratio of the lengths of two wires A and B of same material is 1 : 2 and the ratio of their diameter is 2 : 1. They are stretched by the same force, then the ratio of increase in length will be

2:1

1:4

1:8

8:1

## Questions 4 of 50

Question:The Young's modulus of a wire of length L and radius r is Y N/$$^2$$ . If the length and radius are reduced to L/2 and r/2, then its Young's modulus will be

Y/2

Y

2Y

4Y

## Questions 5 of 50

Question:A beam of metal supported at the two ends is loaded at the centre. The depression at the centre is proportional to

$${Y^2}$$

Y

1/Y

$$1/{Y^2}$$

## Questions 6 of 50

Question:The diameter of a brass rod is 4 mm and Young's modulus of brass is $$9 \times {10^{10}}\,N/{m^2}$$. The force required to stretch by 0.1% of its length is

$$360\,\pi N$$

36 N

$$144\pi \times {10^3}N$$

$$36\pi \times {10^5}N$$

## Questions 7 of 50

Question:If x longitudinal strain is produced in a wire of Young's modulus y, then energy stored in the material of the wire per unit volume is

$$y{x^2}$$

$$2\,y{x^2}$$

$$\frac{1}{2}{y^2}x$$

$$\frac{1}{2}y{x^2}$$

## Questions 8 of 50

Question:In a wire of length L, the increase in its length is l. If the length is reduced to half, the increase in its length will be

l

2l

$$\frac{l}{2}$$

None of the above

## Questions 9 of 50

Question:The Young's modulus of a rubber string 8 cm long and density $$1.5\,kg/{m^3}$$ is $$5 \times {10^8}\,N/{m^2}$$, is suspended on the ceiling in a room. The increase in length due to its own weight will be

$$9.6 \times {10^{ - 5}}\,m$$

$$9.6 \times {10^{ - 11}}\,m$$

$$9.6 \times {10^{ - 3}}\,m$$

9.6 m

## Questions 10 of 50

Question:Two wires of copper having the length in the ratio 4 : 1 and their radii ratio as 1 : 4 are stretched by the same force. The ratio of longitudinal strain in the two will be

01:16

16:1

0.09

64:1:0

## Questions 11 of 50

Question:A weight of 200 kg is suspended by vertical wire of length 600.5 cm. The area of cross-section of wire is $$1\,m{m^2}$$. When the load is removed, the wire contracts by 0.5 cm. The Young's modulus of the material of wire will be

$$2.35 \times {10^{12}}\,N/{m^2}$$

$$1.35 \times {10^{10}}\,N/{m^2}$$

$$13.5 \times {10^{11}}\,N/{m^2}$$

$$23.5 \times {10^9}\,N/{m^2}$$

## Questions 12 of 50

Question:If a load of 9 kg is suspended on a wire, the increase in length is 4.5 mm. The force constant of the wire is

$$0.49 \times {10^4}\,N/m$$

$$1.96 \times {10^4}\,N/m$$

$$4.9 \times {10^4}\,N/m$$

$$0.196 \times {10^4}\,N/m$$

## Questions 13 of 50

Question:The ratio of diameters of two wires of same material is n : 1. The length of wires are 4 m each. On applying the same load, the increase in length of thin wire will be

$${n^2}$$ Times

n times

2n times

None of the above

## Questions 14 of 50

Question:For silver, Young's modulus is $$7.25 \times {10^{10}}\,N/{m^2}$$ and Bulk modulus is $$11 \times {10^{10}}\,N/{m^2}$$. Its Poisson's ratio will be

1

0.5

0.39

0.25

## Questions 15 of 50

Question:The longitudinal strain is only possible in

Gases

Fluids

Solids

Liquids

## Questions 16 of 50

Question:If the density of the material increases, the value of Young's modulus

Increases

Decreases

First increases then decreases

First decreases then increases

## Questions 17 of 50

Question:Young's modulus of rubber is $${10^4}\,N/{m^2}$$ and area of cross-section is $$2\,c{m^2}$$. If force of $$2 \times {10^5}$$dynes is applied along its length, then its initial length l becomes

3L

4L

2L

None of the above

## Questions 18 of 50

Question:Two wires of the same material have lengths in the ratio 1 : 2 and their radii are in the ratio $$1:\sqrt 2$$. If they are stretched by applying equal forces, the increase in their lengths will be in the ratio

$$2:\sqrt 2$$

$$\sqrt 2 :2$$

01:01

01:02

## Questions 19 of 50

Question:When a weight of 10 kg is suspended from a copper wire of length 3 metres and diameter 0.4 mm, its length increases by 2.4 cm. If the diameter of the wire is doubled, then the extension in its length will be

9.6 cm

4.8 cm

1.2 cm

0.6 cm

## Questions 20 of 50

Question:A force of $${10^3}$$ newton stretches the length of a hanging wire by 1 millimetre. The force required to stretch a wire of same material and length but having four times the diameter by 1 millimetre is

$$4 \times {10^3}$$N

$$16 \times {10^3}$$N

$$\frac{1}{4} \times {10^3}$$N

$$\frac{1}{{16}} \times {10^3}$$N

## Questions 21 of 50

Question:Two wires â€˜Aâ€™ and â€˜Bâ€™ of the same material have radii in the ratio 2 : 1 and lengths in the ratio 4 : 1. The ratio of the normal forces required to produce the same change in the lengths of these two wires is

1:1

2:1

1:4

1:2

## Questions 22 of 50

Question:In which case there is maximum extension in the wire, if same force is applied on each wire

L = 500 cm, d = 0.05 mm

L = 200 cm, d = 0.02 mm

L = 300 cm, d = 0.03 mm

L = 400 cm, d = 0.01 mm

## Questions 23 of 50

Question:If a spring is extended to length l, then according to Hook's law

$$F = kl$$

$$F = \frac{k}{l}$$

$$F = {k^2}l$$

$$F = \frac{{{k^2}}}{l}$$

## Questions 24 of 50

Question:Which of the following affects the elasticity of a substance

Hammering and annealing

Change in temperature

Impurity in substance

All of these

## Questions 25 of 50

Question:An iron rod of length 2m and cross section area of $$50\,m{m^2}$$, stretched by 0.5 mm, when a mass of 250 kg is hung from its lower end. Young's modulus of the iron rod is

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

$$19.6 \times {10^{15}}\,N/{m^2}$$

$$19.6 \times {10^{18}}\,N/{m^2}$$

$$19.6 \times {10^{20}}\,N/{m^2}$$

## Questions 26 of 50

Question:The length of an elastic string is a metre when the longitudinal tension is 4 N and b metre when the longitudinal tension is 5 N. The length of the string in metre when the longitudinal tension is 9 N is

$$a - b$$

$$5b - 4a$$

$$2b - \frac{1}{4}a$$

$$4a - 3b$$

## Questions 27 of 50

Question:Stress to strain ratio is equivalent to

Modulus of elasticity

Poission's Ratio

Reyhold number

Fund number

## Questions 28 of 50

Question:Which is correct relation

$$Y < \sigma$$

$$Y > \sigma$$

$$Y = \sigma$$

$$\sigma = + 1$$

## Questions 29 of 50

Question:If the interatomic spacing in a steel wire is 3.0Ã… and $${Y_{steel}}$$= $$20 \times {10^{10}}N/{m^2}$$ then force constant is

$$6 \times {10^{ - 2}}\,N/{\AA}$$

$$6 \times {10^{ - 9}}N/{\AA}$$

$$4 \times {10^{ - 5}}\,N/{\AA}$$

$$6 \times {10^{ - 5}}N/{\AA}$$

## Questions 30 of 50

Question:Minimum and maximum values of Poissonâ€™s ratio for a metal lies between

$$- \infty$$ to +$$\infty$$

0 to 1

$$- \infty \,$$to 1

0 to 0.5

## Questions 31 of 50

Question:A wire of diameter 1mm breaks under a tension of 1000 N. Another wire, of same material as that of the first one, but of diameter 2 mm breaks under a tension of

500 N

1000 N

10000 N

4000 N

## Questions 32 of 50

Question:Youngâ€™s modulus of perfectly rigid body material is

Zero

Infinity

$${\rm{1}} \times {\rm{1}}{{\rm{0}}^{{\rm{10}}}}\,N/{m^2}$$

$${\rm{10}} \times {\rm{1}}{{\rm{0}}^{{\rm{10}}}}\,N/{m^2}$$

## Questions 33 of 50

Question:A wire of length 2 m is made from $$10\;c{m^3}$$ of copper. A force F is applied so that its length increases by 2 mm. Another wire of length 8 m is made from the same volume of copper. If the force F is applied to it, its length will increase by

0.8 cm

1.6 cm

2.4 cm

3.2 cm

## Questions 34 of 50

Question:The ratio of the adiabatic to isothermal elasticities of a triatomic gas is

4/3

1

5/3

3/4

## Questions 35 of 50

Question:If the volume of the given mass of a gas is increased four times, the temperature is raised from 27$$^\circ$$C to 127$$^\circ$$C. The elasticity will become

4 times

1/4 times

3 times

1/3 times

## Questions 36 of 50

Question:The compressibility of water is $$4 \times {10^{ - 5}}$$ per unit atmospheric pressure. The decrease in volume of 100 cubic centimeter of water under a pressure of 100 atmosphere will be

0.4 cc

$$4 \times {10^{ - 5}}\,cc$$

0.025 cc

0.004 cc

## Questions 37 of 50

Question:If a rubber ball is taken at the depth of 200 m in a pool, its volume decreases by 0.1%. If the density of the water is $$1 \times {10^3}\,kg/{m^3}$$ and $$g = 10\,m/{s^2}$$, then the volume elasticity in $$N/{m^2}$$ will be

$${10^8}$$

$$2 \times {10^8}$$

$${10^9}$$

$$2 \times {10^9}$$

## Questions 38 of 50

Question:For a constant hydraulic stress on an object, the fractional change in the object's volume$$\left( {\frac{{\Delta V}}{V}} \right)$$and its bulk modulus (B) are related as

$$\frac{{\Delta V}}{V} \propto \frac{1}{B}$$

$$\frac{{\Delta V}}{V} \propto {B^2}$$

$$\frac{{\Delta v}}{v} \propto {B^{ - 2}}$$

$$\frac{{\Delta V}}{V} \propto B$$

## Questions 39 of 50

Question:Modulus of rigidity of diamond is

Too less

Greater than all matters

Less than all matters

Zero

## Questions 40 of 50

Question:The ratio of lengths of two rods A and B of same material is 1 : 2 and the ratio of their radii is 2 : 1, then the ratio of modulus of rigidity of A and B will be

4:1

16:1

8:1

1:1

## Questions 41 of 50

Question:Which statement is true for a metal

$$Y < \eta$$

$$Y = \eta$$

$$Y > \eta$$

$$Y < 1/\eta$$

## Questions 42 of 50

Question:A 2 m long rod of radius 1 cm which is fixed from one end is given a twist of 0.8 radians. The shear strain developed will be

0

0

0.01

0.02

## Questions 43 of 50

Question:A rod of length l and radius r is joined to a rod of length l/2 and radius r/2 of same material. The free end of small rod is fixed to a rigid base and the free end of larger rod is given a twist of $$\theta ^\circ$$, the twist angle at the joint will be

$$\theta /4$$

$$\theta /2$$

$$5\theta /6$$

$$8\theta /9$$

## Questions 44 of 50

Question:Shearing stress causes change in

Length

Shape

Volume

## Questions 45 of 50

Question:If the potential energy of a spring is V on stretching it by 2 cm, then its potential energy when it is stretched by 10 cm will be

V/25

5V

V/5

25V

## Questions 46 of 50

Question:The Young's modulus of a wire is Y. If the energy per unit volume is E, then the strain will be

$$\sqrt {\frac{{2E}}{Y}}$$

$$\sqrt {2EY}$$

EY

$$\frac{E}{Y}$$

## Questions 47 of 50

Question:The ratio of Young's modulus of the material of two wires is 2 : 3. If the same stress is applied on both, then the ratio of elastic energy per unit volume will be

03:02

02:03

03:04

04:03

## Questions 48 of 50

Question:The length of a rod is 20 cm and area of cross-section $$2\,c{m^2}$$. The Young's modulus of the material of wire is $$1.4 \times {10^{11}}\,N/{m^2}$$. If the rod is compressed by 5 kg-wt along its length, then increase in the energy of the rod in joules will be

$$8.57 \times {10^{ - 6}}$$

$$22.5 \times {10^{ - 4}}$$

$$9.8 \times {10^{ - 5}}$$

$$45.0 \times {10^{ - 5}}$$

## Questions 49 of 50

Question:If a spring extends by x on loading, then the energy stored by the spring is (if T is tension in the spring and k is spring constant)

$$\frac{{{T^2}}}{{2x}}$$

$$\frac{{{T^2}}}{{2k}}$$

$$\frac{{2x}}{{{T^2}}}$$

$$\frac{{2{T^2}}}{k}$$

## Questions 50 of 50

Question:Wires A and B are made from the same material. A has twice the diameter and three times the length of B. If the elastic limits are not reached, when each is stretched by the same tension, the ratio of energy stored in A to that in B is