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If the total radial interference between two cylinders forming a compound cylinder is δ and Young's modulus of the materials of the cylinders is E, then the interface pressure developed at the interface between two cylinders of the same material and same length is:
- a)Directly proportional of E x δ
- b)Inversely proportional of E/ δ
- c)Directly proportional of E/ δ
- d)Inversely proportional of E / δ
Correct answer is option 'A'. Can you explain this answer?
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Explanation:
To understand why the interface pressure developed at the interface between two cylinders of the same material and same length is directly proportional to Young's modulus (E), let's break down the concept and analyze it step by step.
1. Radial Interference:
When two cylinders are combined to form a compound cylinder, there will be a certain amount of radial interference between them. Radial interference refers to the difference in radius between the outer surface of the inner cylinder and the inner surface of the outer cylinder. It can be calculated by subtracting the radius of the inner cylinder from the radius of the outer cylinder.
2. Interface Pressure:
The radial interference between the cylinders creates a contact pressure at the interface. This contact pressure is known as the interface pressure. It is the force per unit area acting perpendicular to the interface between the cylinders.
3. Relationship with Young's Modulus:
Young's modulus (E) is a measure of the stiffness or rigidity of a material. It quantifies how much a material deforms under an applied force. It is defined as the ratio of stress to strain.
Now, let's consider the relationship between interface pressure and Young's modulus.
- If the Young's modulus of the material is high, it means the material is stiffer or more rigid. In this case, the material will resist deformation and will require a higher force to cause a given amount of deformation.
- On the other hand, if the Young's modulus is low, the material will be more flexible and will deform more easily under an applied force.
4. Direct Proportionality:
Based on the above understanding, we can conclude that the interface pressure developed at the interface between the cylinders is directly proportional to Young's modulus (E). This means that as the Young's modulus increases, the interface pressure will also increase. Similarly, if the Young's modulus decreases, the interface pressure will decrease.
Therefore, the correct answer is option 'A' - the interface pressure developed at the interface between two cylinders of the same material and same length is directly proportional to Young's modulus (E).
Summary:
- The interface pressure developed at the interface between two cylinders is directly proportional to Young's modulus (E).
- Young's modulus quantifies the stiffness or rigidity of a material.
- A higher Young's modulus indicates a stiffer material, which requires a higher force to cause deformation.
- A lower Young's modulus indicates a more flexible material, which deforms more easily under an applied force.
To understand why the interface pressure developed at the interface between two cylinders of the same material and same length is directly proportional to Young's modulus (E), let's break down the concept and analyze it step by step.
1. Radial Interference:
When two cylinders are combined to form a compound cylinder, there will be a certain amount of radial interference between them. Radial interference refers to the difference in radius between the outer surface of the inner cylinder and the inner surface of the outer cylinder. It can be calculated by subtracting the radius of the inner cylinder from the radius of the outer cylinder.
2. Interface Pressure:
The radial interference between the cylinders creates a contact pressure at the interface. This contact pressure is known as the interface pressure. It is the force per unit area acting perpendicular to the interface between the cylinders.
3. Relationship with Young's Modulus:
Young's modulus (E) is a measure of the stiffness or rigidity of a material. It quantifies how much a material deforms under an applied force. It is defined as the ratio of stress to strain.
Now, let's consider the relationship between interface pressure and Young's modulus.
- If the Young's modulus of the material is high, it means the material is stiffer or more rigid. In this case, the material will resist deformation and will require a higher force to cause a given amount of deformation.
- On the other hand, if the Young's modulus is low, the material will be more flexible and will deform more easily under an applied force.
4. Direct Proportionality:
Based on the above understanding, we can conclude that the interface pressure developed at the interface between the cylinders is directly proportional to Young's modulus (E). This means that as the Young's modulus increases, the interface pressure will also increase. Similarly, if the Young's modulus decreases, the interface pressure will decrease.
Therefore, the correct answer is option 'A' - the interface pressure developed at the interface between two cylinders of the same material and same length is directly proportional to Young's modulus (E).
Summary:
- The interface pressure developed at the interface between two cylinders is directly proportional to Young's modulus (E).
- Young's modulus quantifies the stiffness or rigidity of a material.
- A higher Young's modulus indicates a stiffer material, which requires a higher force to cause deformation.
- A lower Young's modulus indicates a more flexible material, which deforms more easily under an applied force.
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If the total radial interference between two cylinders forming a compound cylinder is δ and Young's modulus of the materials of the cylinders is E, then the interface pressure developed at the interface between two cylinders of the same material and same length is:a)Directly proportional of E x δb)Inversely proportional of E/ δc)Directly proportional of E/ δd)Inversely proportional of E / δCorrect answer is option 'A'. Can you explain this answer?
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If the total radial interference between two cylinders forming a compound cylinder is δ and Young's modulus of the materials of the cylinders is E, then the interface pressure developed at the interface between two cylinders of the same material and same length is:a)Directly proportional of E x δb)Inversely proportional of E/ δc)Directly proportional of E/ δd)Inversely proportional of E / δCorrect answer is option 'A'. Can you explain this answer? for Mechanical Engineering 2024 is part of Mechanical Engineering preparation. The Question and answers have been prepared according to the Mechanical Engineering exam syllabus. Information about If the total radial interference between two cylinders forming a compound cylinder is δ and Young's modulus of the materials of the cylinders is E, then the interface pressure developed at the interface between two cylinders of the same material and same length is:a)Directly proportional of E x δb)Inversely proportional of E/ δc)Directly proportional of E/ δd)Inversely proportional of E / δCorrect answer is option 'A'. Can you explain this answer? covers all topics & solutions for Mechanical Engineering 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If the total radial interference between two cylinders forming a compound cylinder is δ and Young's modulus of the materials of the cylinders is E, then the interface pressure developed at the interface between two cylinders of the same material and same length is:a)Directly proportional of E x δb)Inversely proportional of E/ δc)Directly proportional of E/ δd)Inversely proportional of E / δCorrect answer is option 'A'. Can you explain this answer?.
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