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Which of the following conditions are to be satisfied by a two-mass system which is dynamically equivalent to a rigid body?
1. The total mass should be equal to that of the rigid body.
2. The centre of gravity should coincide with that of the rigid body.
3. The total moment of inertia about an axis through the centre of gravity must be equal to that of the rigid body.
2. The centre of gravity should coincide with that of the rigid body.
3. The total moment of inertia about an axis through the centre of gravity must be equal to that of the rigid body.
Select the correct answer using the codes given below:
- a)1 and 2
- b)2 and 3
- c)1 and 3
- d)None of the above
Correct answer is option 'C'. Can you explain this answer?
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Verified Answer
Which of the following conditions are to be satisfied by a two-mass sy...
A is false. The centre of gravity of the two masses should coincide with that of the rigid body.
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Which of the following conditions are to be satisfied by a two-mass sy...
Explanation:
A two-mass system is said to be dynamically equivalent to a rigid body when it behaves in the same way as a rigid body under the action of external forces and moments. In other words, the system should exhibit the same translational and rotational motion as a rigid body.
To satisfy this condition, the following criteria must be met:
1. The total mass should be equal to that of the rigid body:
For a two-mass system to be dynamically equivalent to a rigid body, the total mass of the system should be equal to the mass of the rigid body. This ensures that the system has the same inertia as the rigid body and will respond to external forces in the same way.
2. The centre of gravity should coincide with that of the rigid body:
The centre of gravity of a system is the point at which the entire weight of the system can be considered to act. For a two-mass system to be dynamically equivalent to a rigid body, the centre of gravity of the system should coincide with the centre of gravity of the rigid body. This ensures that the system will undergo the same translational motion as a rigid body when subjected to external forces.
3. The total moment of inertia about an axis through the centre of gravity must be equal to that of the rigid body:
The moment of inertia is a measure of an object's resistance to rotational motion. For a two-mass system to be dynamically equivalent to a rigid body, the total moment of inertia of the system about an axis passing through the centre of gravity should be equal to the moment of inertia of the rigid body about the same axis. This ensures that the system will undergo the same rotational motion as a rigid body when subjected to external moments.
Therefore, all three conditions must be satisfied for a two-mass system to be dynamically equivalent to a rigid body. The correct answer is option C, which states that conditions 1 and 3 should be satisfied.
A two-mass system is said to be dynamically equivalent to a rigid body when it behaves in the same way as a rigid body under the action of external forces and moments. In other words, the system should exhibit the same translational and rotational motion as a rigid body.
To satisfy this condition, the following criteria must be met:
1. The total mass should be equal to that of the rigid body:
For a two-mass system to be dynamically equivalent to a rigid body, the total mass of the system should be equal to the mass of the rigid body. This ensures that the system has the same inertia as the rigid body and will respond to external forces in the same way.
2. The centre of gravity should coincide with that of the rigid body:
The centre of gravity of a system is the point at which the entire weight of the system can be considered to act. For a two-mass system to be dynamically equivalent to a rigid body, the centre of gravity of the system should coincide with the centre of gravity of the rigid body. This ensures that the system will undergo the same translational motion as a rigid body when subjected to external forces.
3. The total moment of inertia about an axis through the centre of gravity must be equal to that of the rigid body:
The moment of inertia is a measure of an object's resistance to rotational motion. For a two-mass system to be dynamically equivalent to a rigid body, the total moment of inertia of the system about an axis passing through the centre of gravity should be equal to the moment of inertia of the rigid body about the same axis. This ensures that the system will undergo the same rotational motion as a rigid body when subjected to external moments.
Therefore, all three conditions must be satisfied for a two-mass system to be dynamically equivalent to a rigid body. The correct answer is option C, which states that conditions 1 and 3 should be satisfied.
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Which of the following conditions are to be satisfied by a two-mass system which is dynamically equivalent to a rigid body?1. The total mass should be equal to that of the rigid body.2. The centre of gravity should coincide with that of the rigid body.3. The total moment of inertia about an axis through the centre of gravity must be equal to that of the rigid body.Select the correct answer using the codes given below:a)1 and 2b)2 and 3c)1 and 3d)None of the aboveCorrect answer is option 'C'. Can you explain this answer?
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Which of the following conditions are to be satisfied by a two-mass system which is dynamically equivalent to a rigid body?1. The total mass should be equal to that of the rigid body.2. The centre of gravity should coincide with that of the rigid body.3. The total moment of inertia about an axis through the centre of gravity must be equal to that of the rigid body.Select the correct answer using the codes given below:a)1 and 2b)2 and 3c)1 and 3d)None of the aboveCorrect 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 Which of the following conditions are to be satisfied by a two-mass system which is dynamically equivalent to a rigid body?1. The total mass should be equal to that of the rigid body.2. The centre of gravity should coincide with that of the rigid body.3. The total moment of inertia about an axis through the centre of gravity must be equal to that of the rigid body.Select the correct answer using the codes given below:a)1 and 2b)2 and 3c)1 and 3d)None of the aboveCorrect 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 Which of the following conditions are to be satisfied by a two-mass system which is dynamically equivalent to a rigid body?1. The total mass should be equal to that of the rigid body.2. The centre of gravity should coincide with that of the rigid body.3. The total moment of inertia about an axis through the centre of gravity must be equal to that of the rigid body.Select the correct answer using the codes given below:a)1 and 2b)2 and 3c)1 and 3d)None of the aboveCorrect answer is option 'C'. Can you explain this answer?.
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