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If a two-mass system is dynamically equivalent to a rigid body, then the system will NOT satisfy the condition that the
- a)Sum of the two masses must be equal to that of the rigid body
- b)Polar moment of inertia of the system should be equal to that of the rigid body
- c)Centre of gravity (c.g.) of the system should coincide with that of the rigid body
- d)Total moment of inertia about the axis through c.g. must be equal to that of the rigid body
Correct answer is option 'D'. Can you explain this answer?
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If a two-mass system is dynamically equivalent to a rigid body, then t...
Dynamically Equivalent Two-Mass System and Rigid Body
Heading: Definition of Dynamically Equivalent Two-Mass System
A two-mass system is said to be dynamically equivalent to a rigid body when the system exhibits the same dynamic behavior as that of a rigid body. In other words, the system has the same natural frequencies of vibration and the same mode shapes as that of a rigid body.
Heading: Conditions for Dynamically Equivalent Two-Mass System
To satisfy the condition of dynamic equivalence between a two-mass system and a rigid body, the following conditions must be met:
1. The sum of the two masses must be equal to that of the rigid body.
2. The polar moment of inertia of the system should be equal to that of the rigid body.
3. The center of gravity (c.g.) of the system should coincide with that of the rigid body.
4. The total moment of inertia about the axis through c.g. must be equal to that of the rigid body.
Heading: Explanation of the Correct Answer
The correct answer to the given question is option 'D' which states that the total moment of inertia about the axis through c.g. must be equal to that of the rigid body. This condition is not satisfied in a dynamically equivalent two-mass system.
A two-mass system can be considered dynamically equivalent to a rigid body if it satisfies all the conditions mentioned above. However, the total moment of inertia about the axis through c.g. cannot be equal to that of the rigid body because the two-mass system has two separate masses with different moments of inertia.
Therefore, a dynamically equivalent two-mass system cannot satisfy the condition that the total moment of inertia about the axis through c.g. must be equal to that of the rigid body, which is why option 'D' is the correct answer.
Heading: Definition of Dynamically Equivalent Two-Mass System
A two-mass system is said to be dynamically equivalent to a rigid body when the system exhibits the same dynamic behavior as that of a rigid body. In other words, the system has the same natural frequencies of vibration and the same mode shapes as that of a rigid body.
Heading: Conditions for Dynamically Equivalent Two-Mass System
To satisfy the condition of dynamic equivalence between a two-mass system and a rigid body, the following conditions must be met:
1. The sum of the two masses must be equal to that of the rigid body.
2. The polar moment of inertia of the system should be equal to that of the rigid body.
3. The center of gravity (c.g.) of the system should coincide with that of the rigid body.
4. The total moment of inertia about the axis through c.g. must be equal to that of the rigid body.
Heading: Explanation of the Correct Answer
The correct answer to the given question is option 'D' which states that the total moment of inertia about the axis through c.g. must be equal to that of the rigid body. This condition is not satisfied in a dynamically equivalent two-mass system.
A two-mass system can be considered dynamically equivalent to a rigid body if it satisfies all the conditions mentioned above. However, the total moment of inertia about the axis through c.g. cannot be equal to that of the rigid body because the two-mass system has two separate masses with different moments of inertia.
Therefore, a dynamically equivalent two-mass system cannot satisfy the condition that the total moment of inertia about the axis through c.g. must be equal to that of the rigid body, which is why option 'D' is the correct answer.
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If a two-mass system is dynamically equivalent to a rigid body, then the system will NOT satisfy the condition that the a)Sum of the two masses must be equal to that of the rigid bodyb)Polar moment of inertia of the system should be equal to that of the rigid bodyc)Centre of gravity (c.g.) of the system should coincide with that of the rigid bodyd)Total moment of inertia about the axis through c.g. must be equal to that of the rigid bodyCorrect answer is option 'D'. Can you explain this answer?
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If a two-mass system is dynamically equivalent to a rigid body, then the system will NOT satisfy the condition that the a)Sum of the two masses must be equal to that of the rigid bodyb)Polar moment of inertia of the system should be equal to that of the rigid bodyc)Centre of gravity (c.g.) of the system should coincide with that of the rigid bodyd)Total moment of inertia about the axis through c.g. must be equal to that of the rigid bodyCorrect answer is option 'D'. 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 a two-mass system is dynamically equivalent to a rigid body, then the system will NOT satisfy the condition that the a)Sum of the two masses must be equal to that of the rigid bodyb)Polar moment of inertia of the system should be equal to that of the rigid bodyc)Centre of gravity (c.g.) of the system should coincide with that of the rigid bodyd)Total moment of inertia about the axis through c.g. must be equal to that of the rigid bodyCorrect answer is option 'D'. 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 a two-mass system is dynamically equivalent to a rigid body, then the system will NOT satisfy the condition that the a)Sum of the two masses must be equal to that of the rigid bodyb)Polar moment of inertia of the system should be equal to that of the rigid bodyc)Centre of gravity (c.g.) of the system should coincide with that of the rigid bodyd)Total moment of inertia about the axis through c.g. must be equal to that of the rigid bodyCorrect answer is option 'D'. Can you explain this answer?.
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