Free Young's Modulus and Stress-Strain MCQs with Answers
11 Young's Modulus and Stress-Strain MCQs from Physics, each with the correct answer and a written explanation of why it is correct. Free and unlimited, with no account needed.
Stress and strain describe how a solid deforms under an applied force, while Young's modulus is the ratio of tensile stress to tensile strain within the elastic limit. The topic includes elastic and plastic behaviour, Hooke's law, the stress strain graph and the difference between stiffness, strength and breaking stress.
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1. if both the length and radius of the rod are doubled, then modulus of elasticity will:
- A. inerease
- B. Deerease
- C. Remains the same
- D. Be doubled
Explanation: When the length ( L ) and radius ( r ) of a rod are doubled, the new length and radius are ( 2L ) and ( 2r ) respectively. The modulus of elasticity ( E ) is defined as the ratio of stress to strain, and is given by: E= Stress/StrainBy solving it, we find that modulus of elasticity become half.But it is an intrinsic property of a material, meaning it does not change with the dimensions of the material. Therefore, if both the length and radius of the rod are doubled, the modulus of elasticity will remain unchanged.
Correct answer: Remains the same2. A force of 500 N is applied to one end of a cylindrical steel rod of diameter 50cm, the tensile stress is;
- A. 1.5 x 10^5Nm- 2
- B. 2.5 x 10^5Nm- 2
- C. 2.5 x 10^3Nm- 2
- D. 1 x 10^5Nm- 2
Explanation: We use the formula: σ= F/A Given:Force (F) = 500 NDiameter of the rod = 50 cm = 0.5 mThe cross-sectional area of a cylinder is calculated using the formula for the area of a circle ( A = πr2 ), where ( r ) is the radius of the circle.The radius is half of the diameter, so:r =0.5m/2 =0.25mNow, we can calculate the area:A = π(0.25)2 = π(0.0625 = 0.19635m² (rounded to 5 decimal places)Finally, we can calculate the tensile stress: σ = 500/0.19635 = 2546.48 Nm-2So, the tensile stress is approximately 2546.48 or 2.5×103Nm- 2.
Correct answer: 2.5 x 10^3Nm- 23. Which of the following is the Young Modulus of steel?
- A. 20 x 10^9N/m2
- B. 3.9 x 10^-9N/m2
- C. 2 x 10^11N/m2
- D. 1.5 x 10^9N/m2
Explanation: The young modulus of steel is 20×1010 Pa which is 20×109N/m2.
Correct answer: 20 x 10^9N/m24. A wire is stretched to four times of its length its strain is
- A. 0.5
- B. 4
- C. 3
- D. 1
Explanation: As, Strain= ΔL/Lwhere, ΔL=4L-L=3LSo, the strain is: Strain= ΔL/L =3L/L =3So, the strain is 3. This is a unitless quantity as it is a ratio of lengths.
Correct answer: 35. If a material becomes more resistant to shear deformation, then shear modulus will
- A. increase.
- B. decrease.
- C. become zero.
- D. remain constant.
Explanation: A higher shear modulus indicates that a material is more resistant to shear deformation. Conversely, a material that is easily deformed under shear stress will have a lower shear modulus.Conclusion:Therefore, if a material becomes more resistant to shear deformation, its shear modulus will increase.
Correct answer: increase.6. The dimension of Young's Modulus is:
- A. M2L-1T2
- B. ML-1T-1
- C. ML-1T-2
- D. ML-2T-2
Explanation: Young's modulus is the slope of the initial section of the curve (i.e. m in y = mx + b). When a material reaches a certain stress, the material will begin to deform. It is up to a point where the structure of the material is stretching and not deforming. Unit of Young's Modulus =N/m2=kgm/s2m2=ms2kg=ML−1T−2.
Correct answer: ML-1T-27. Volume stress divided by volume strain equal to:
- A. Young's modulus
- B. Bulk modulus
- C. Shear modulus
- D. Hyper modulus
Explanation: Bulk modulus is the ratio or hydrostatic stress to the volumetric strain. Within the elastic range is called bulk modulus. It is denoted by K or B. Sometimes referred to as the incompressibility, the bulk modulus is a measure of the ability of a substance to withstand changes in volume when under compression on all sides. It is equal to the quotient of the applied pressure divided by the relative deformation.
Correct answer: Bulk modulus8. Hook's law correlates the:
- A. Force and displacement
- B. Force and extension
- C. Force and compression
- D. Stress and strain
Explanation: Hooke's Law is a principle of physics that states the strain in a solid is proportional to the applied stress within the elastic limit of that material. Mathematically, it can be expressed as Stress/Strain = Constant. This means that the material will return to its original shape after the stress is removed, as long as the elastic limit is not surpassed. The other options mention relationships that are not the fundamental focus of Hooke's Law. While force can influence displacement, extension, and compression, Hooke's Law specifically addresses the proportional relationship between stress and strain.
Correct answer: Stress and strain9. A vertical steel wire X of circular cross-section is used to suspend a load. A second wire Y, made of the same material but having twice the length and twice the diameter is used to suspend an equal load. What is the value of the ratio?
- A. 1/1
- B. 1
- C. 2
- D. 4
Explanation: Since the wires at made of the same material, their young modulus will be the same hence they have the same length, force and area. So the ratio is going to be 1/1 = 1
Correct answer: 1/110. The shear modulus of elasticity G is:
- A. Option A
- B. Option B
- C. Option C
- D. Option D
Explanation: The shear modulus of elasticity/rigidity G is a material's ability to resist deformation, it is defined as the ratio of tangential stress to the shearing strain within the elastic limit. It can be understood better by the following (where y=θ).
Correct answer: Option CYoung's Modulus and Stress-Strain MCQs: common questions
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