Mechanical Engineering Exam > Mechanical Engineering Questions > Consider the following statements:When two sp...
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Consider the following statements:
When two springs of equal lengths are arranged to form a cluster spring
1. Angle of twist in both the springs will be equal
2. Deflection of both the springs will be equal
3. Load taken by each spring will be half the total load
4. Shear stress in each spring will be equal
Which of the above statements is/are correct?
- a)1 and 2
- b)3 and 4
- c)2 only
- d)4 only
Correct answer is option 'A'. Can you explain this answer?
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Statement Analysis:
The given statements are related to the behavior of a cluster spring made up of two equal-length springs. We need to analyze each statement individually to determine their correctness.
Statement 1: Angle of twist in both the springs will be equal
The angle of twist in a spring is determined by the applied torque and the torsional stiffness of the spring. Since both springs are of equal length, they will have the same torsional stiffness. Therefore, when the same torque is applied to both springs, the angle of twist will be equal.
Statement 2: Deflection of both the springs will be equal
The deflection of a spring is determined by the applied load and the stiffness of the spring. Since both springs are of equal length, they will have the same stiffness. Therefore, when the same load is applied to both springs, the deflection will be equal.
Statement 3: Load taken by each spring will be half the total load
When two equal-length springs are arranged in a cluster spring, they share the load equally. This is because the load is distributed between the two springs based on their stiffness. Since both springs are of equal stiffness, they will each take half of the total load.
Statement 4: Shear stress in each spring will be equal
The shear stress in a spring is determined by the applied torque and the cross-sectional area of the spring. Since both springs are of equal length and material, they will have the same cross-sectional area. Therefore, when the same torque is applied to both springs, the shear stress will be equal.
Conclusion:
Based on the analysis of the statements, we can conclude that:
- Statement 1 is correct because the angle of twist in both springs will be equal.
- Statement 2 is correct because the deflection of both springs will be equal.
- Statement 3 is correct because the load taken by each spring will be half the total load.
- Statement 4 is incorrect because the shear stress in each spring will depend on the torque applied, not the length or arrangement of the springs.
Therefore, the correct answer is option 'A' - 1 and 2.
The given statements are related to the behavior of a cluster spring made up of two equal-length springs. We need to analyze each statement individually to determine their correctness.
Statement 1: Angle of twist in both the springs will be equal
The angle of twist in a spring is determined by the applied torque and the torsional stiffness of the spring. Since both springs are of equal length, they will have the same torsional stiffness. Therefore, when the same torque is applied to both springs, the angle of twist will be equal.
Statement 2: Deflection of both the springs will be equal
The deflection of a spring is determined by the applied load and the stiffness of the spring. Since both springs are of equal length, they will have the same stiffness. Therefore, when the same load is applied to both springs, the deflection will be equal.
Statement 3: Load taken by each spring will be half the total load
When two equal-length springs are arranged in a cluster spring, they share the load equally. This is because the load is distributed between the two springs based on their stiffness. Since both springs are of equal stiffness, they will each take half of the total load.
Statement 4: Shear stress in each spring will be equal
The shear stress in a spring is determined by the applied torque and the cross-sectional area of the spring. Since both springs are of equal length and material, they will have the same cross-sectional area. Therefore, when the same torque is applied to both springs, the shear stress will be equal.
Conclusion:
Based on the analysis of the statements, we can conclude that:
- Statement 1 is correct because the angle of twist in both springs will be equal.
- Statement 2 is correct because the deflection of both springs will be equal.
- Statement 3 is correct because the load taken by each spring will be half the total load.
- Statement 4 is incorrect because the shear stress in each spring will depend on the torque applied, not the length or arrangement of the springs.
Therefore, the correct answer is option 'A' - 1 and 2.
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Consider the following statements:When two springs of equal lengths are arranged to form a cluster spring1. Angle of twist in both the springs will be equal2. Deflection of both the springs will be equal3. Load taken by each spring will be half the total load4. Shear stress in each spring will be equalWhich of the above statements is/are correct?a)1 and 2 b)3 and 4 c)2 onlyd)4 onlyCorrect answer is option 'A'. Can you explain this answer?
Question Description
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