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If two shafts of the same length, one of which is hollow, transmit equal torque and have equal maximum stress, then they should have equal
- a)Polar moment of inertia
- b)Polar modulus of section
- c)Diameter
- d)Angie of twist
Correct answer is option 'B'. Can you explain this answer?
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Verified Answer
If two shafts of the same length, one of which is hollow, transmit equ...
As Ts = Th,
∴ Zs = Zh
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If two shafts of the same length, one of which is hollow, transmit equ...
Polar Modulus of Section
The polar modulus of section is a property that relates to the resistance of a shaft to torsional deformation. It represents the stiffness of a shaft in resisting twisting or torsion. The polar modulus of section is denoted by the symbol "Zp" and is a measure of the shaft's resistance to torsional deformation.
Torque Transmission and Maximum Stress
When two shafts of the same length transmit equal torque and have equal maximum stress, it means that they have the same capacity to handle the applied torque without experiencing excessive deformation or failure. This implies that both shafts have similar torsional rigidity.
Relationship between Polar Modulus of Section and Torsional Rigidity
The torsional rigidity of a shaft, which is a measure of its resistance to torsional deformation, is directly proportional to its polar modulus of section. In other words, the greater the polar modulus of section, the stiffer the shaft will be and the more torque it can transmit without significant deformation.
Role of Hollow Shaft in Torsional Rigidity
A hollow shaft has a larger polar modulus of section compared to a solid shaft of the same outer diameter. This is because the presence of material near the outer edges of the shaft contributes more to its resistance to torsional deformation than the material near the center. By removing material from the center and keeping the outer diameter constant, the polar modulus of section increases, resulting in a stiffer shaft.
Conclusion
In the given scenario, if two shafts of the same length transmit equal torque and have equal maximum stress, it implies that they have the same torsional rigidity. Since the torsional rigidity is directly related to the polar modulus of section, it can be concluded that the two shafts also have equal polar modulus of section. Therefore, option B, which states that the two shafts have equal polar modulus of section, is the correct answer.
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If two shafts of the same length, one of which is hollow, transmit equal torque and have equal maximum stress, then they should have equala)Polar moment of inertiab)Polar modulus of sectionc)Diameterd)Angie of twistCorrect answer is option 'B'. Can you explain this answer?
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