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The shear stress at a point in a shaft subjected to a torque is:
- a)Directly proportional to the polar moment of inertia and to the distance of the point form the axis
- b)Directly proportional to the applied torque and inversely proportional to the polar moment of inertia.
- c)Directly proportional to the applied torque and polar moment of inertia
- d)inversely proportional to the applied torque and the polar moment of inertia
Correct answer is option 'B'. Can you explain this answer?
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Shear stress in a shaft subjected to a torque
Explanation:
When a shaft is subjected to a torque, shear stress is developed within the material. Shear stress is defined as the force per unit area perpendicular to the axis of the shaft. In other words, it is the internal resistance within the material to the applied torque.
Direct proportionality to the applied torque:
The shear stress in a shaft is directly proportional to the applied torque. This means that as the torque increases, the shear stress also increases. This is because a higher torque exerts a greater force on the shaft, leading to higher shear stress.
Inversely proportional to the polar moment of inertia:
The polar moment of inertia is a measure of an object's resistance to torsional deformation. It depends on the geometry of the shaft and is directly related to the distribution of material around the central axis. The larger the polar moment of inertia, the greater the resistance to deformation.
Shear stress is inversely proportional to the polar moment of inertia. This means that as the polar moment of inertia increases, the shear stress decreases. A larger polar moment of inertia indicates a greater resistance to deformation, resulting in lower shear stress.
Combining the factors:
When considering both the applied torque and the polar moment of inertia together, we can conclude that the shear stress is directly proportional to the applied torque and inversely proportional to the polar moment of inertia.
This relationship can be mathematically expressed as:
Shear stress ∝ Torque / Polar moment of inertia
Therefore, option B is the correct answer as it correctly describes the relationship between shear stress, torque, and polar moment of inertia.
Explanation:
When a shaft is subjected to a torque, shear stress is developed within the material. Shear stress is defined as the force per unit area perpendicular to the axis of the shaft. In other words, it is the internal resistance within the material to the applied torque.
Direct proportionality to the applied torque:
The shear stress in a shaft is directly proportional to the applied torque. This means that as the torque increases, the shear stress also increases. This is because a higher torque exerts a greater force on the shaft, leading to higher shear stress.
Inversely proportional to the polar moment of inertia:
The polar moment of inertia is a measure of an object's resistance to torsional deformation. It depends on the geometry of the shaft and is directly related to the distribution of material around the central axis. The larger the polar moment of inertia, the greater the resistance to deformation.
Shear stress is inversely proportional to the polar moment of inertia. This means that as the polar moment of inertia increases, the shear stress decreases. A larger polar moment of inertia indicates a greater resistance to deformation, resulting in lower shear stress.
Combining the factors:
When considering both the applied torque and the polar moment of inertia together, we can conclude that the shear stress is directly proportional to the applied torque and inversely proportional to the polar moment of inertia.
This relationship can be mathematically expressed as:
Shear stress ∝ Torque / Polar moment of inertia
Therefore, option B is the correct answer as it correctly describes the relationship between shear stress, torque, and polar moment of inertia.
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The shear stress at a point in a shaft subjected to a torque is:a)Directly proportional to the polar moment of inertia and to the distance of the point form the axisb)Directly proportional to the applied torque and inversely proportional to the polar moment of inertia.c)Directly proportional to the applied torque and polar moment of inertiad)inversely proportional to the applied torque and the polar moment of inertiaCorrect answer is option 'B'. Can you explain this answer?
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The shear stress at a point in a shaft subjected to a torque is:a)Directly proportional to the polar moment of inertia and to the distance of the point form the axisb)Directly proportional to the applied torque and inversely proportional to the polar moment of inertia.c)Directly proportional to the applied torque and polar moment of inertiad)inversely proportional to the applied torque and the polar moment of inertiaCorrect answer is option 'B'. 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 The shear stress at a point in a shaft subjected to a torque is:a)Directly proportional to the polar moment of inertia and to the distance of the point form the axisb)Directly proportional to the applied torque and inversely proportional to the polar moment of inertia.c)Directly proportional to the applied torque and polar moment of inertiad)inversely proportional to the applied torque and the polar moment of inertiaCorrect answer is option 'B'. 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 The shear stress at a point in a shaft subjected to a torque is:a)Directly proportional to the polar moment of inertia and to the distance of the point form the axisb)Directly proportional to the applied torque and inversely proportional to the polar moment of inertia.c)Directly proportional to the applied torque and polar moment of inertiad)inversely proportional to the applied torque and the polar moment of inertiaCorrect answer is option 'B'. Can you explain this answer?.
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