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Physics Case study (4 Marks)

Mechanical Properties of Solids · UP Board (UPMSP) STD 11 Science (UPMSP - English Medium). 6 questions.

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Case study (4 Marks)

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6 questions · self-marked practice — reveal the answer and mark yourself.

Question 14 Marks
Read the passage given below and answer the following questions from 1 to 5. The property of a body, by virtue of which it tends to regain its original size and shape when the applied force is removed, is known as elasticity and the deformation caused is known as elastic deformation. However, if you apply force to a lump of putty or mud, they have no gross tendency to regain their previous shape, and they get permanently deformed. Such substances are called plastic and this property is called plasticity. Putty and mud are close to ideal plastics. We know that in a solid, each atom or molecule is surrounded by neighboring atoms or molecules. These are bonded together by interatomic or intermolecular forces and stay in a stable equilibrium position. When a solid is deformed, the atoms or molecules are displaced from their equilibrium positions causing a change in the interatomic (or intermolecular) distances. When the deforming force is removed, the interatomic forces tend to drive them back to their original positions. Thus the body regains its original shape and size. Answer the following
  1. Putty and mud are example of:
  1. Ideal plastic
  2. Ideal elastic
  3. Pseudo plastic
  4. None of these
  1. The property of a body, by virtue of which it tends to regain its original size and shape when the applied force is removed, is known as:
  1. Elasticity
  2. Plasticity
  3. Both
  4. None of these
  1. Define elasticity.
  1. Define plasticity.
  1. Explain elastic behavior of solid.
Answer
  1. (a) Ideal plastic
  1. (a) Elasticity
  1. The property of a body, by virtue of which it tends to regain its original size and shape when the applied force is removed, is known as elasticity and the deformation caused is known as elastic deformation.
  1. The property of a body, in which body does not regain its original size and shape when the applied force is removed and get permanently deformed, is known as plasticity.
  1. We know that in a solid, each atom or molecule is surrounded by neighboring atoms or molecules. These are bonded together by interatomic or intermolecular forces and stay in a stable equilibrium position. When a solid is deformed, the atoms or molecules are displaced from their equilibrium positions causing a change in the interatomic (or intermolecular) distances. When the deforming force is removed, the interatomic forces tend to drive them back to their original positions. Thus the body regains its original shape and size.
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Question 24 Marks
Read the passage given below and answer the following questions from 1 to 5. Stress-Strain Curve The graph shown below shows qualitatively the relation between the stress and the strain as the deformation gradually increases. Within Hooke’s limit for a certain region stress and strain relation is linear. Beyond that up to a certain value of strain the body is still elastic and if deforming forces are removed the body recovers its original shape.
  1. If deforming forces are removed up to which point the curve will be retraced?
  1. Upto OA only
  2. Upto OB
  3. Upto C
  4. Never retraced its path
  1. In the above question, during loading and unloading the force exerted by the material are conservative up to:
  1. OA only
  2. OB only
  3. OC only
  4. OD only
  1. During unloading beyond B, say C, the length at zero stress in now equal to:
  1. Less than original length
  2. Greater than original length
  3. Original length
  4. Can’t be predicted
  1. The breaking stress for a wire of unit cross - section is called:
  1. Yield point
  2. Elastic fatigue
  3. Tensile strength
  4. Young’s modulus
  1. Substances which can be stretched to cause large strains are called:
  1. Isomers
  2. Plastomers
  3. Elastomers
  4. Polymers
Answer
  1. (b) Upto OB
  1. (b) OB only
Explanation:
Point Bis the elastic limit.
  1. (b) Greater than original length
Explanation:
Beyond B even if deforming forces are removed still some deformation is left.
  1. (c) Tensile strength
Explanation:
The breaking stress for a wire of unit cross-section is called tensile strength.
  1. (c) Elastomers
Explanation:
Substances which can be stretched to cause large Strains are called elastomers.
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Question 34 Marks
Read the passage given below and answer the following questions from 1 to 5. The proportional region within the elastic limit of the stress-strain curve is of great importance for structural and manufacturing engineering designs. The ratio of stress and strain, called modulus of elasticity, is found to be a characteristic of the material. Experimental observation show that for a given material, the magnitude of the strain produced is same whether the stress is tensile or compressive. The ratio of tensile (or compressive) stress $(\sigma)$ to the longitudinal strain $(\in)$ is defined as Young’s modulus and is denoted by the symbol Y. $\text{Y}=\frac{\sigma}{\in}$ Since strain is a dimensionless quantity, the unit of Young’s modulus is the same as that of stress i.e., $N-m^{-2}$ or Pascal (Pa). As steel has more modulus of elasticity than copper brass and aluminum hence steel is preferred in heavy-duty machines and in structural designs. Wood, bone, concrete and glass have rather small Young’s moduli. Answer the following.
  1. If stress strain changes then young’s modulus is:
  1. Also changes.
  2. Remains constant.
  3. Either changes or remains constant depends on amount of stress and strain.
  4. None of these.
  1. SI unit of young’s modulus is:
  1. $N-m^{-2}​​​​​​​$
  2. Pascal (Pa).
  3. $N-m^{-2}​​​​​​​$​​​​​​​ or Pascal (Pa).
  4. None of these
  1. Which of the following is more elastic
  1. Aluminum
  2. Steel
  3. Wood
  4. Glass
  1. Defines young’s modulus. Give its SI unit and dimensions.
  1. Why steel is more preferred in heavy industries than copper and brass?
Answer
  1. (b) Remains constant.
  1. (c) $N-m^{-2}$​​​​​​​ or Pascal (Pa).
  1. (b) Steel
  1. The ratio of tensile (or compressive) stress $(\sigma)$ to the longitudinal strain $(\in)$ is defined as Young’s modulus and is denoted by the symbol Y.
$\text{Y}=\frac{\sigma}{\in}$
the unit of Young’s modulus is the same as that of stress i.e., $N-m^{-2} $ or Pascal (Pa) and its dimensional formula is $[ML^{-1} T^{-2}]​​​​​​​$​​​​​​​
  1. Steel is more preferred in heavy industries than copper and brass because steel has more modulus of elasticity that is higher young’s modulus than copper and brass. In short steel is more elastic than copper and brass.
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Question 44 Marks
Read the passage given below and answer the following questions from 1 to 5. For small deformations within elastic limit the stress and strain are proportional to each other. This is known as Hooke’s law. Thus, stress α strain Stress = k × strain Where k is the proportionality constant and is known as modulus of elasticity. Hooke’s law is an empirical law and is found to be valid for most materials. However, there are some materials which do not exhibit this linear relationship.

 In the region from A to B, stress and strain are not proportional. Nevertheless, the body still returns to its original dimension when the load is removed. The point B in the curve is known as yield point (also known as elastic limit) and the corresponding stress is known as yield strength $(\sigma _y)$ of the material. If the load is increased further, the stress developed exceeds the yield strength and strain increases rapidly even for a small change in the stress. The portion of the curve between B and D shows this. When the load is removed, say at some point C between B and D, the body does not regain its original dimension. In this case, even when the stress is zero, the strain is not zero. The material is said to have a permanent set. The deformation is said to be plastic deformation. The point D on the graph is the ultimate tensile strength $(\sigma _u)$ of the material. Beyond this point, additional strain is produced even by a reduced applied force and fracture occurs at point E. If the ultimate strength and fracture points D and E are close, the material is said to be brittle. If they are far apart, the material is said to be ductile.
  1. Stress is directly proportional to strain this is valid:
  1. Above elastic limit
  2. Within elastic limit
  3. Above plastic limit
  4. None of these
  1. SI unit of modulus of elasticity is:
  1. $N/m^2$
  2. N
  3. No unit
  4. None of these
  1. Define modulus of elasticity.
  1. State hooks law.
  1. Write note on stress strain curve for ductile material.
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Question 54 Marks
Read the passage given below and answer the following questions from 1 to 5. According to Hooke’s law, within the elastic limit, the stress applied to a body is directly proportional to the corresponding strain. $\text{Stress}\propto\text{Strain}$ or Stress = E × Strain or $\frac{\text{Stress }}{\text{Strain}}=\text{E}$ Where E is the constant of proportionality and is known as coefficient of elasticity or modulus of elasticity. Hooke’s law is an empirical law and is found to be valid for most materials. However, there are some materials which do not exhibit this linear relationship.
  1. According to Hooke’s law of elasticity, if stress is increased, the ratio of stress to strain:
  1. Decreases
  2. Increases
  3. Becomes zero
  4. Remains constant
  1. Within elastic limit, which of the following graphs correctly represents the variation of extension in the length of a wire with the external load?
  1. According to Hooke’s law, ifstressis reduced to one-third, the ratio of stress to strain:
  1. Is increased to three time
  2. Is decreased
  3. Is zero
  4. Remains constant.
  1. Hooke’s law defines:
  1. Stress
  2. Strain
  3. Modulus of elasticity
  4. Elastic limit.
  1. Whenever a material is loaded with elasitic limits, stress is ......... strain.
  1. Equal to
  2. Directly proportional to
  3. Inxessely propotional to
  4. None of the above given remains constant.
Answer
  1. (d) Remains constant
Explanation:
According to Hooke’s law, within the elastic limit, stress is directly proportional! to the strain i.e.
$\text{Stress}\propto\text{Strain}$ or Stress = k strain $\frac{\text{Stress }}{\text{Strain}}=\text{k}$ where k is the proportionality constant and is known as modulus of elasticity.
  1. (b)
Explanation:
According to Hooke's law, Within elastic limit, $\text{Extension}\propto\text{Load applied}$ Hence, option (b) represents the correct graph.
  1. (d) Remains constant.
  1. (c) Modulus of elasticity
Explanation:
Hooke's law gives the relation between stress and strain, which is given by the modulus of elasticity.
  1. (b) Directly proportional to
Explanation:
When a spring balance has been used for a long time, the spring in the balance fatigued and there is loss of strength of the spring.
In such a case, the extension in the spring is more for a given load and hence the balance gives wrong readings.
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Question 64 Marks
Read the passage given below and answer the following questions from 1 to 5. When a body is subjected to a deforming force, a restoring force is developed in the body. This restoring force is equal in magnitude but opposite in direction to the applied force. The restoring force per unit area is known as stress. If F is the force applied normal to the cross–section and A is the area of cross section of the body. Magnitude of the stress $=\frac{\text{F}}{\text{A}}$ The SI unit of stress is $N-m^{-2}$ or Pascal (Pa) and its dimensional formula is $[ML^{-1} T^{-2}]$. The restoring force per unit area in this case is called tensile stress. If the cylinder is compressed under the action of applied forces, the restoring force per unit area is known as compressive stress. Tensile or compressive stress can also be termed as longitudinal stress. In both the cases, there is a change in the length of the cylinder. The change in the length ΔL to the original length L of the body is known as longitudinal strain. The restoring force per unit area developed due to the applied tangential force is known as tangential or shearing stress.
  1. Restoring force per unit area is called as:
  1. Stress
  2. Strain
  3. Modulus of elasticity
  4. None of these
  1. Ratio of change in dimension to original dimension is called:
  1. Stress
  2. Strain
  3. Modulus of elasticity
  4. None of these
  1. Define shear stress.
  1. Define stress. Give its SI unit and dimension.
  1. Define strain. Give its SI unit and dimension
Answer
  1. (a) Stress
  1. (b) Strain
  1. The tangential restoring force per unit area developed known as tangential or shearing stress.
  1. When a body is subjected to a deforming force, a restoring force is developed in the body. This restoring force is equal in magnitude but opposite in direction to the applied force. The restoring force per unit area is known as stress.
If F is the force applied normal to the cross–section and A is the area of cross section of the body.
Magnitude of the stress $=\frac{\text{F}}{\text{A}}$
The SI unit of stress is $N-m^{-2}$ or Pascal (Pa) and its dimensional formula is $[ML^{-1} T^{-2}]$.
  1. Ratio of change in dimension to original dimension is called strain. As it is ratio of similar quantities so it carries no unit and hence no dimensions.
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