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Mechanical Properties of Solids Class 11 MCQs Questions with Answers
Multiple Choice Type Questions
Question 1.
The fractional change in volume per unit increase in the pressure is called :
(a) Volume coefficient
(b) Pressure gradient
(c) Compressibility
(d) Bulk modulus
Answer
Answer: (c) Compressibility
Question 2.
A thick rope of density ρ and length l is hung from a rigid support. The Young’s modulus of the material of rope is Y. The increase in length of the rope due to its own weight is
(a) \(\frac {ρgl}{Y}\)
(b) \(\frac {ρgl^2}{Y}\)
(c) \(\frac {1}{2}\) \(\frac {ρgl^2}{Y}\)
(d) \(\frac {1}{4}\) \(\frac {ρgl^2}{Y}\)
Answer
Answer: (c) \(\frac {1}{2}\) \(\frac {ρgl^2}{Y}\)
Question 3.
You are given two wires W1 and W2. Both are made of the same material and are of the same length. The radius of cross-section of W2 is twice that of W1. Same load is suspended from both of them. If the strain in W1 be 4, then calculate the strain in W2.
(a) 8
(b) 4
(c) 2
(d) 1
Answer
Answer: (d) 1
Question 4.
A wire of length L and radius r fixed at one end and a force F applied to the other end produces an extension l. The extension produced in another wire of same material of length 2L and radius 2r by a force 2F is given by
(a) l
(b) 2l
(c) \(\frac {l}{2}\)
(d) 4l
Answer
Answer: (a) l
Question 5.
A steel wire is loaded by 2 kg weight. If the radius of the wire is doubled, then its extension will become
(a) half
(b) four times
(c) one-fourth
(d) double
Answer
Answer: (c) one-fourth
Question 6.
A cable breaks if stretched by more than 2 mm. It is cut into two equal parts. By how much either part can be stretched without breaking?
(a) 2mm
(b) 1 mm
(c) 0.5 mm
(d) 0.25 mm
Answer
Answer: (b) 1 mm
Question 7.
In the following data, the fou r wires made of the same material have length L and radius r. Which 6f these will have the maximum extension when the same force is applied?
(a) L = 50 cm, r = 0.4 mm
(b) L = 100 cm, r = 1 mm
(c) L = 200 cm, r = 2 mm
(d) L = 300 cm, r = 3 mm
Answer
Answer: (a) L = 50 cm, r = 0.4 mm
Question 8.
According to Hook’s law, the force required to change the length of a wife by l is proportional to
(a) l
(b) l²
(c) l-1
(d) l-2
Answer
Answer: (a) l
Question 9.
The energy per unit volume of a strained wire is given by
(a) \(\frac {1}{2}\) stress × strain
(b) \(\frac {1}{2}\) strain × load
(c) \(\frac {1}{2}\) extension × stress
(d) \(\frac {1}{2}\) load × extension
Answer
Answer: (a) \(\frac {1}{2}\) stress × strain
Question 10.
The energy stored in the strained wire is given by
(a) \(\frac {1}{2}\) stress × strain
(b) \(\frac {1}{2}\) strain × load
(c) \(\frac {1}{2}\) extension × stress
(d) \(\frac {1}{2}\) load × extension
Answer
Answer: (d) \(\frac {1}{2}\) load × extension
Question 11.
The graph between the applied force and the change in length of a wire within elastic limit is a
(a) straight line with zero slope
(b) straight line with positive slope
(c) straight line with negative slope
(d) all of the above
Answer
Answer: (b) straight line with positive slope
Question 12.
For obtaining appreciable extension, the wire must be
(a) short and thin
(b) long and thick
(c) long and thin
(d) short and thick
Answer
Answer: (c) long and thin
Question 13.
The Young’s modulus of air is
(a) zero
(b) infinity
(c) more han 1 but not infinity
(d) less than 1 but not zero
Answer
Answer: (a) zero
Question 14.
How does the Young’s modulus vary with the increase of temperature?
(a) increases
(b) decreases
(c) remains constant
(d) first increases and then decreases
Answer
Answer: (b) decreases
Question 15.
The Young’s modulus of a perfectly rigid body is
(a) one
(b) infinity
(c) zero
(d) none of the above
Answer
Answer: (b) infinity
Question 16.
The modulus of rigidity of water is
(a) one
(b) infinity
(c) zero
(d) none of the above
Answer
Answer: (c) zero
Question 17.
The bulk modulus of a perfectly rigid body is
(a) one
(b) infinity
(c) zero
(d) none of the above
Answer
Answer: (b) infinity
Question 18.
If both the length and radius of the wire are doubled, then how does the modulus of elasticity change?
(a) doubled
(b) halved
(c) becomes one fourth
(d) remains unchanged
Answer
Answer: (d) remains unchanged
Question 19.
A cable which can support a load W is cut into two equal parts. The maximum load that can be supported by either part is
(a) W
(b) 2W
(c) \(\frac {W}{2}\)
(d) \(\frac {W}{4}\)
Answer
Answer: (a) W
Question 20.
The substance which shows no elastic after effect practically is
(a) steel
(b) rubber
(c) copper
(d) quartz
Answer
Answer: (d) quartz
Question 21.
Two wires A and B are of the same material, but A is half as long and has diameter three times the diameter of wire B. If they are stretched by the same amount, then the required force in wire A must be
(a) three times that on B
(b) one third that on B
(c) nine times that on B
(d) eighteen times that on B
Answer
Answer: (d) eighteen times that on B
Question 22.
The breaking stress for wire of unit area of cross-section is called its:
(a) Young’s modulus
(b) tensile strength
(c) yield point
(d) elastic limit
Answer
Answer: (b) tensile strength
Question 23.
The breaking stress of a material is defined as
(a) breaking load per unit area
(b) breaking load per unit volume
(c) breaking load per unit length
(d) total breaking load
Answer
Answer: (a) breaking load per unit area
Question 24.
The maximum length of the steel wire (of density ρ = 7.8 × 10³, kg/m³) which when fixed at one end can hang freely without breaking (breaking stress for steel is 7.8 × 108 Nm-2) is (take g = 10 ms-2):
(a) 1 km
(b) 0.01 km
(c) 0.1 km
(d) 10 km
Answer
Answer: (d) 10 km
Question 25.
Girders are made in I shape to
(a) increase its strength
(b) make it appear more elegant
(c) reduce the quantity of material used
(d) none of the above
Answer
Answer: (c) reduce the quantity of material used
Fill in the blanks
Question 1.
…………….. is defined as the lagging behind the strain from
Answer
Answer: Elastic hysteresis.
Question 2.
A volumetric strain is equivalent to …………….. mutually perpendicular linear strains, each equal in magnitude to …………….. of the volumetric strain.
Answer
Answer: three, one-third.
Question 3
…………….. is called a point upto which Hook’s law is strictly Obeyed.
Answer
Answer: Proportional limit.
Question 4
The increase in the length of a wire for virtually no increase in the stress is called ……………..
Answer
Answer: plastic behaviour.
Question 5.
…………….. is a point at which the wire begins to flow.
Answer
Answer: Yield point.
Question 6.
…………….. is also called ultimate stress and the product of breaking stress and the area of cross-section is called ……………..
Answer
Answer: Breaking stress, breaking load.
Question 7.
…………….. is defined as the reciprocal of the bulk modulus of a material.
Answer
Answer: Compressibility.
Question 8.
A wire increases by 10-6 of its length when a stress of 108 Nmf is app lied to it. So Young’s modulus of the material is ……………..
Answer
Answer: 1014 Nm-2.
Question 9.
A wire of length L and cross-sectional are A is made of a material of Young’s modulus Y. If the wire is stretched by an amount x, then the work done is ……………..
Answer
Answer: \(\frac {AYx^2}{2L}\)
Question 10.
…………….. is defined as the delay in regaining the original state by a body after the removal of the deforming forces.
Answer
Answer: Elastic after effect.
True/False Type Questions
1. Which of the following statement is True/False?
(a) Extension of a wire is inversely proportional to cross-section A.
(b) Extension of a wire is directly proportional to Young’s modulus.
(c) Extension is inversely proportion to the original length of the wire.
Answer
Answer:
(a) True
(b) False
(c) False
2. Which of the following statement is True/False?
(a) The breaking stress is independent of the length of a wire.
(b) The breaking stress depends upon the^rea of cross-section of the wire.
(c) Breaking stress is called elastic limit.
Answer
Answer:
(a) True
(b) True
(c) False
3. Which of the following statement is True/False?
(a) For more longitudinal extension with the same mass, the body must be in the form of a long thin wire.
(b) A body which does not undergo any deformation when subjected to a set of balanced forces is called a rigid body.
(c) A body is perfectly elastic if it recovers its original shape or volume on the removal of the deforming force.
Answer
Answer:
(a) True
(b) True
(c) True
4. Tell which of the following statements are True/False?
(а) Steel is more elastic than rubber.
(b) Quartz is an almost perfectly elastic body.
(c) A liquid has infinite value of the modulus of rigidity.
Answer
Answer:
(a) True
(b) True
(c) False
5. Tell which of the following statements are True/False?
(a) Steel is preferred for making spring over copper because Young’s modulus of steel is more than, that of copper.
(b) Breaking load for unit area of cross-section of a wire is called tensile strength.
(c) The dimensional formula for stress is same as that for pressure.
Answer
Answer:
(a) True
(b) False
(c) True
6. Tell which of the following statements are True/False about steel being for elastic than rubber?
(a) Young’s modulus of steel is much larger than that of rubber.
(b) For given load, there is more strain in rubber than in steel.
(c) For given strain, there is more stress in steel than in rubber.
(d) Steel wire returns to original length when load is removed but rubber does not do so.
Answer
Answer:
(a) True
(b) True
(c) True
(d) False
7. Which of the, following statements are True/False?
(a) Glass is more elastic than rubber.
(b) Young’s modulus decreases with rise in temperature.
(c) Breaking stress of thicker wire of same material is more.
Answer
Answer:
(a) True
(b) True
(c) False
8. Which of the following is True/False?
(a) A wire is shortened to half of its original length. Then its elongation under a given load will be half the former amount.
(b) The strain persists even when the stress is removed and thus lags behind the stress.
(c) The bulk modulus of an incompressible liquid is zero.
Answer
Answer:
(a) True
(b) True
(c) False
9. Which of the following statements are True/False?
(a) The’elastomers are the elastic substances which can be subjected to large value of strain Le. greatly stretched e.g.- rubber.
(b) The work done in stretching the wire is stored in it in the form of elastic potential energy.
(c) The modulus of rigidity of water is zero.
Answer
Answer:
(a) True
(b) True
(c) True.
10. Select True/False?
The factors affecting the property of elasticity of a solid are
(a) Change in temperature.
(b) Effect of hammering rolling and annealing.
(c) Presence of impurities. the stress.
Answer
Answer:
(a) True
(b) True
(c) True.
Match the following
| Column I | Column II |
| (a) Young’s modulus of a perfectly rigid body | (i) zero |
| (b) Modulus of rigidity of water | (ii) infinity |
| (c) Strain of a wire stretched to double its length | (iii) 1 |
Answer
Answer:
| Column I | Column II |
| (a) Young’s modulus of a perfectly rigid body | (ii) infinity |
| (b) Modulus of rigidity of water | (i) zero |
| (c) Strain of a wire stretched to double its length | (iii) 1 |
| Column I | Column II |
| (a) Young’s modulus of air | (i) infinity |
| (b) Bulk modulus of a perfectly rigid body | (ii) Young’s modulus |
| (c) It decreases with temperature | (iii) zero |
Answer
Answer:
| Column I | Column II |
| (a) Young’s modulus of air | (iii) zero |
| (b) Bulk modulus of a perfectly rigid body | (i) infinity |
| (c) It decreases with temperature | (ii) Young’s modulus |
| Column I | Column II |
| (a) Con possibility of a perfectly rigid body | (i) Nm-2 or Pa |
| (b) S.I. unit of coefficient of elasticity | (ii) zero |
| (c) C.G.S. unit of Y | (iii) dyne cm-2 |
Answer
Answer:
| Column I | Column II |
| (a) Con possibility of a perfectly rigid body | (ii) zero |
| (b) S.I. unit of coefficient of elasticity | (i) Nm-2 or Pa |
| (c) C.G.S. unit of Y | (iii) dyne cm-2 |
| Column I | Column II |
| (a) Materials which can be drawn in the form of a wire | (i) brittle |
| (b) Materials which break on increasing stress beyond the elastic limit | (ii) elastomers |
| (c) Materials having large elastic limit | (iii) ductile |
Answer
Answer:
| Column I | Column II |
| (a) Materials which can be drawn in the form of a wire | (iii) ductile |
| (b) Materials which break on increasing stress beyond the elastic limit | (i) brittle |
| (c) Materials having large elastic limit | (ii) elastomers |
| Column I | Column II |
| (a) Stress is proportional to strain | (i) elastic limit |
| (b) The graph between stress and strain is obtained on unloading the wire | (ii) permanent set |
| (c) Residual strain left in the wire which is said to have been permanently deformed | (iii) proportional limit |
Answer
Answer:
| Column I | Column II |
| (a) Stress is proportional to strain | (iii) proportional limit |
| (b) The graph between stress and strain is obtained on unloading the wire | (i) elastic limit |
| (c) Residual strain left in the wire which is said to have been permanently deformed | (ii) permanent set |
| Column I | Column II |
| (a) The point at which the wire yields to the applied stress and goes on increasing in length even if load is kept constant. | (i) ductile |
| (b) The material for which plastic range is relatively longer and they are permanently deformed before breaking | (ii) brittle |
| (c) A material which has relatively Smaller plastic range and breaks as soon as elastic limit is crossed. | (iii) yield point |
Answer
Answer:
| Column I | Column II |
| (a) The point at which the wire yields to the applied stress and goes on increasing in length even if load is kept constant. | (iii) yield point |
| (b) The material for which plastic range is relatively longer and they are permanently deformed before breaking | (i) ductile |
| (c) A material which has relatively Smaller plastic range and breaks as soon as elastic limit is crossed. | (ii) brittle |
| Column I | Column II |
| (a) Dimensional formula of modulus of rigidity | (i) Hook’s law |
| (b) Dimensional formula of compressibility | (ii) [M-1 L T²] |
| (c) Stres ∝ strain | (iii) [M L-1 T-2] |
Answer
Answer:
| Column I | Column II |
| (a) Dimensional formula of modulus of rigidity | (iii) [M L-1 T-2] |
| (b) Dimensional formula of compressibility | (ii) [M-1 L T²] |
| (c) Stres ∝ strain | (i) Hook’s law |
| Column I | Column II |
| (a) Restoring force acting per unit area perpendicular to the surface of the body | (i) plasticity |
| (b) Restoring force acting per unit area tangential to the surface of the body | (ii) elasticity |
| (c) Property of bodies due to which they regain their original dimensions fully after the removal of deforming forces | (iii) tangential stress |
| (d) Property of due to which they can’t regain their original dimensions on removal of the deforming forces | (iv) normal stress |
Answer
Answer:
| Column I | Column II |
| (a) Restoring force acting per unit area perpendicular to the surface of the body | (iv) normal stress |
| (b) Restoring force acting per unit area tangential to the surface of the body | (iii) tangential stress |
| (c) Property of bodies due to which they regain their original dimensions fully after the removal of deforming forces | (ii) elasticity |
| (d) Property of due to which they can’t regain their original dimensions on removal of the deforming forces | (i) plasticity |
| Column I | Column II |
| (a) The force which changes or tends to change the dimensions of a body | (i) compressional stress |
| (b) The force which brings or tends to bring the body to its original state | (ii) tensile stress |
| (c) Normal stress which increases the length or volume of the body | (iii) restoring force |
| (d) Normal stress which decreases the length or volume of the body | (iv) deforming force |
Answer
Answer:
| Column I | Column II |
| (a) The force which changes or tends to change the dimensions of a body | (iv) deforming force |
| (b) The force which brings or tends to bring the body to its original state | (iii) restoring force |
| (c) Normal stress which increases the length or volume of the body | (ii) tensile stress |
| (d) Normal stress which decreases the length or volume of the body | (i) compressional stress |
| Column I | Column II |
| (a) Have definite shape and size | (i) liquids |
| (b) They do not possess a definite shape but possess a definite volume | (ii) gases |
| (c) They don’t have definite shape or volume | (iii) solids |
Answer
Answer:
| Column I | Column II |
| (a) Have definite shape and size | (iii) solids |
| (b) They do not possess a definite shape but possess a definite volume | (i) liquids |
| (c) They don’t have definite shape or volume | (ii) gases |
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