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Two shafts, one of solid section and the other of hollow section, of same materia) and weight having same length are subjected to equal torsional force. What is the torsional stiffness of hollow shaft?
- a)Equal to that of the solid shaft
- b)Less than that of the solid shaft
- c)More than that of the solid shaft
- d)Exactly half of that of the solid shaft
Correct answer is option 'C'. Can you explain this answer?
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Verified Answer
Two shafts, one of solid section and the other of hollow section, of s...
Let the diameter of solid shaft be ds. Let the external and internal diameter of the hollow shaft be d0 and di respectively.
it is given that both the shafts are made of same material, have same weight and length and are subjected to equal torsional force.
∴ Weight of solid shaft = Weight of hollow shaft
Now, we know that, torsional stiffness is given as
For same value of G and L
[from (i)]
Now, the quantity
is always greater than 1
∴ Kh > Ks
it is given that both the shafts are made of same material, have same weight and length and are subjected to equal torsional force.
∴ Weight of solid shaft = Weight of hollow shaft
Now, we know that, torsional stiffness is given as
For same value of G and L
[from (i)]
Now, the quantity
is always greater than 1∴ Kh > Ks
Most Upvoted Answer
Two shafts, one of solid section and the other of hollow section, of s...
Torsional Stiffness of Hollow Shaft Compared to Solid Shaft
The torsional stiffness of a shaft is defined as the torque required to produce a unit twist per unit length. It is a measure of the shaft's resistance to twisting. When two shafts of the same material and weight but different cross-sectional areas are subjected to equal torsional force, their torsional stiffness will be different. Here's why the torsional stiffness of a hollow shaft is more than that of a solid shaft:
Cross-Sectional Area
The cross-sectional area of a hollow shaft is less than that of a solid shaft of the same weight and length. This means that the hollow shaft has more material distributed towards its outer perimeter than the solid shaft. The outer perimeter of a shaft experiences a greater shear stress than the inner portion. Therefore, the hollow shaft is better equipped to resist torsional loads than the solid shaft.
Polar Moment of Inertia
The polar moment of inertia is a property of a cross-sectional area that measures its resistance to torsional loads. The polar moment of inertia of a hollow shaft is greater than that of a solid shaft of the same weight and length. This is because the material of the hollow shaft is distributed away from its central axis, which increases its polar moment of inertia.
Torsional Stiffness
The torsional stiffness of a shaft is directly proportional to its polar moment of inertia. Therefore, the torsional stiffness of a hollow shaft is more than that of a solid shaft of the same weight and length. This means that the hollow shaft can resist twisting more effectively than the solid shaft.
Conclusion
When two shafts of the same material and weight are subjected to equal torsional force, the torsional stiffness of the hollow shaft is more than that of the solid shaft. This is because the hollow shaft has more material distributed towards its outer perimeter and a higher polar moment of inertia.
The torsional stiffness of a shaft is defined as the torque required to produce a unit twist per unit length. It is a measure of the shaft's resistance to twisting. When two shafts of the same material and weight but different cross-sectional areas are subjected to equal torsional force, their torsional stiffness will be different. Here's why the torsional stiffness of a hollow shaft is more than that of a solid shaft:
Cross-Sectional Area
The cross-sectional area of a hollow shaft is less than that of a solid shaft of the same weight and length. This means that the hollow shaft has more material distributed towards its outer perimeter than the solid shaft. The outer perimeter of a shaft experiences a greater shear stress than the inner portion. Therefore, the hollow shaft is better equipped to resist torsional loads than the solid shaft.
Polar Moment of Inertia
The polar moment of inertia is a property of a cross-sectional area that measures its resistance to torsional loads. The polar moment of inertia of a hollow shaft is greater than that of a solid shaft of the same weight and length. This is because the material of the hollow shaft is distributed away from its central axis, which increases its polar moment of inertia.
Torsional Stiffness
The torsional stiffness of a shaft is directly proportional to its polar moment of inertia. Therefore, the torsional stiffness of a hollow shaft is more than that of a solid shaft of the same weight and length. This means that the hollow shaft can resist twisting more effectively than the solid shaft.
Conclusion
When two shafts of the same material and weight are subjected to equal torsional force, the torsional stiffness of the hollow shaft is more than that of the solid shaft. This is because the hollow shaft has more material distributed towards its outer perimeter and a higher polar moment of inertia.
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Two shafts, one of solid section and the other of hollow section, of same materia) and weight having same length are subjected to equal torsional force. What is the torsional stiffness of hollow shaft?a)Equal to that of the solid shaftb)Less than that of the solid shaftc)More than that of the solid shaftd)Exactly half of that of the solid shaftCorrect answer is option 'C'. Can you explain this answer?
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Two shafts, one of solid section and the other of hollow section, of same materia) and weight having same length are subjected to equal torsional force. What is the torsional stiffness of hollow shaft?a)Equal to that of the solid shaftb)Less than that of the solid shaftc)More than that of the solid shaftd)Exactly half of that of the solid shaftCorrect answer is option 'C'. 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 Two shafts, one of solid section and the other of hollow section, of same materia) and weight having same length are subjected to equal torsional force. What is the torsional stiffness of hollow shaft?a)Equal to that of the solid shaftb)Less than that of the solid shaftc)More than that of the solid shaftd)Exactly half of that of the solid shaftCorrect answer is option 'C'. 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 Two shafts, one of solid section and the other of hollow section, of same materia) and weight having same length are subjected to equal torsional force. What is the torsional stiffness of hollow shaft?a)Equal to that of the solid shaftb)Less than that of the solid shaftc)More than that of the solid shaftd)Exactly half of that of the solid shaftCorrect answer is option 'C'. Can you explain this answer?.
Two shafts, one of solid section and the other of hollow section, of same materia) and weight having same length are subjected to equal torsional force. What is the torsional stiffness of hollow shaft?a)Equal to that of the solid shaftb)Less than that of the solid shaftc)More than that of the solid shaftd)Exactly half of that of the solid shaftCorrect answer is option 'C'. 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 Two shafts, one of solid section and the other of hollow section, of same materia) and weight having same length are subjected to equal torsional force. What is the torsional stiffness of hollow shaft?a)Equal to that of the solid shaftb)Less than that of the solid shaftc)More than that of the solid shaftd)Exactly half of that of the solid shaftCorrect answer is option 'C'. 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 Two shafts, one of solid section and the other of hollow section, of same materia) and weight having same length are subjected to equal torsional force. What is the torsional stiffness of hollow shaft?a)Equal to that of the solid shaftb)Less than that of the solid shaftc)More than that of the solid shaftd)Exactly half of that of the solid shaftCorrect answer is option 'C'. Can you explain this answer?.
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Two shafts, one of solid section and the other of hollow section, of same materia) and weight having same length are subjected to equal torsional force. What is the torsional stiffness of hollow shaft?a)Equal to that of the solid shaftb)Less than that of the solid shaftc)More than that of the solid shaftd)Exactly half of that of the solid shaftCorrect answer is option 'C'. Can you explain this answer?, a detailed solution for Two shafts, one of solid section and the other of hollow section, of same materia) and weight having same length are subjected to equal torsional force. What is the torsional stiffness of hollow shaft?a)Equal to that of the solid shaftb)Less than that of the solid shaftc)More than that of the solid shaftd)Exactly half of that of the solid shaftCorrect answer is option 'C'. Can you explain this answer? has been provided alongside types of Two shafts, one of solid section and the other of hollow section, of same materia) and weight having same length are subjected to equal torsional force. What is the torsional stiffness of hollow shaft?a)Equal to that of the solid shaftb)Less than that of the solid shaftc)More than that of the solid shaftd)Exactly half of that of the solid shaftCorrect answer is option 'C'. Can you explain this answer? theory, EduRev gives you an
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