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Which one of the following statements is correct (a) Parallel and axes theorem are valid for homogeneous as well as non-homogeneous objects (b) 1 axes theorem is applicable for 2d objects but not for 1d objects (c) Parallel axes theorem is applicable for 1d, 2d, 3d objects, but I axes theorem is not applicable for 3d objects. (d) For parallel axes theorem to be applicable one of the two parallel axes must pass through COM?
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Which one of the following statements is correct (a) Parallel and axes...
Correct Statement: (c) Parallel axes theorem is applicable for 1d, 2d, 3d objects, but I axes theorem is not applicable for 3d objects.
Explanation:
The parallel axes theorem and the perpendicular axes theorem are two important concepts in mechanics that are used to determine the moment of inertia of an object about an axis. Let's discuss each statement and determine which one is correct.
(a) Parallel and axes theorem are valid for homogeneous as well as non-homogeneous objects:
This statement is incorrect. The parallel and perpendicular axes theorems are valid only for homogeneous objects. Homogeneous objects have uniform density throughout, whereas non-homogeneous objects have varying density. The theorems rely on the uniformity of the density distribution to simplify the calculation of the moment of inertia.
(b) 1 axes theorem is applicable for 2d objects but not for 1d objects:
This statement is incorrect. The parallel axes theorem, also known as the first moment of inertia theorem, is applicable for both 1-dimensional and 2-dimensional objects. It allows you to calculate the moment of inertia of a 2D object about an axis parallel to and a distance 'd' away from an axis passing through the center of mass (COM) of the object.
(c) Parallel axes theorem is applicable for 1d, 2d, 3d objects, but I axes theorem is not applicable for 3d objects:
This statement is correct. The parallel axes theorem is applicable for objects of any dimensionality, whether it is 1D, 2D, or 3D. It states that the moment of inertia of an object about an axis parallel to and a distance 'd' away from an axis passing through the COM is equal to the moment of inertia about the axis passing through the COM plus the product of the mass of the object and the square of the distance 'd'.
On the other hand, the perpendicular axes theorem, also known as the second moment of inertia theorem or Steiner's theorem, is not applicable for 3D objects. It is only applicable for 2D objects and allows you to calculate the moment of inertia about an axis perpendicular to the plane of the object, given the moment of inertia about an axis parallel to the axis of rotation and passing through the COM.
Conclusion:
The correct statement among the given options is (c). The parallel axes theorem is applicable for 1D, 2D, and 3D objects, while the perpendicular axes theorem is not applicable for 3D objects.
Explanation:
The parallel axes theorem and the perpendicular axes theorem are two important concepts in mechanics that are used to determine the moment of inertia of an object about an axis. Let's discuss each statement and determine which one is correct.
(a) Parallel and axes theorem are valid for homogeneous as well as non-homogeneous objects:
This statement is incorrect. The parallel and perpendicular axes theorems are valid only for homogeneous objects. Homogeneous objects have uniform density throughout, whereas non-homogeneous objects have varying density. The theorems rely on the uniformity of the density distribution to simplify the calculation of the moment of inertia.
(b) 1 axes theorem is applicable for 2d objects but not for 1d objects:
This statement is incorrect. The parallel axes theorem, also known as the first moment of inertia theorem, is applicable for both 1-dimensional and 2-dimensional objects. It allows you to calculate the moment of inertia of a 2D object about an axis parallel to and a distance 'd' away from an axis passing through the center of mass (COM) of the object.
(c) Parallel axes theorem is applicable for 1d, 2d, 3d objects, but I axes theorem is not applicable for 3d objects:
This statement is correct. The parallel axes theorem is applicable for objects of any dimensionality, whether it is 1D, 2D, or 3D. It states that the moment of inertia of an object about an axis parallel to and a distance 'd' away from an axis passing through the COM is equal to the moment of inertia about the axis passing through the COM plus the product of the mass of the object and the square of the distance 'd'.
On the other hand, the perpendicular axes theorem, also known as the second moment of inertia theorem or Steiner's theorem, is not applicable for 3D objects. It is only applicable for 2D objects and allows you to calculate the moment of inertia about an axis perpendicular to the plane of the object, given the moment of inertia about an axis parallel to the axis of rotation and passing through the COM.
Conclusion:
The correct statement among the given options is (c). The parallel axes theorem is applicable for 1D, 2D, and 3D objects, while the perpendicular axes theorem is not applicable for 3D objects.
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Which one of the following statements is correct (a) Parallel and axes theorem are valid for homogeneous as well as non-homogeneous objects (b) 1 axes theorem is applicable for 2d objects but not for 1d objects (c) Parallel axes theorem is applicable for 1d, 2d, 3d objects, but I axes theorem is not applicable for 3d objects. (d) For parallel axes theorem to be applicable one of the two parallel axes must pass through COM?
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Which one of the following statements is correct (a) Parallel and axes theorem are valid for homogeneous as well as non-homogeneous objects (b) 1 axes theorem is applicable for 2d objects but not for 1d objects (c) Parallel axes theorem is applicable for 1d, 2d, 3d objects, but I axes theorem is not applicable for 3d objects. (d) For parallel axes theorem to be applicable one of the two parallel axes must pass through COM? for Physics 2024 is part of Physics preparation. The Question and answers have been prepared according to the Physics exam syllabus. Information about Which one of the following statements is correct (a) Parallel and axes theorem are valid for homogeneous as well as non-homogeneous objects (b) 1 axes theorem is applicable for 2d objects but not for 1d objects (c) Parallel axes theorem is applicable for 1d, 2d, 3d objects, but I axes theorem is not applicable for 3d objects. (d) For parallel axes theorem to be applicable one of the two parallel axes must pass through COM? covers all topics & solutions for Physics 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Which one of the following statements is correct (a) Parallel and axes theorem are valid for homogeneous as well as non-homogeneous objects (b) 1 axes theorem is applicable for 2d objects but not for 1d objects (c) Parallel axes theorem is applicable for 1d, 2d, 3d objects, but I axes theorem is not applicable for 3d objects. (d) For parallel axes theorem to be applicable one of the two parallel axes must pass through COM?.
Which one of the following statements is correct (a) Parallel and axes theorem are valid for homogeneous as well as non-homogeneous objects (b) 1 axes theorem is applicable for 2d objects but not for 1d objects (c) Parallel axes theorem is applicable for 1d, 2d, 3d objects, but I axes theorem is not applicable for 3d objects. (d) For parallel axes theorem to be applicable one of the two parallel axes must pass through COM? for Physics 2024 is part of Physics preparation. The Question and answers have been prepared according to the Physics exam syllabus. Information about Which one of the following statements is correct (a) Parallel and axes theorem are valid for homogeneous as well as non-homogeneous objects (b) 1 axes theorem is applicable for 2d objects but not for 1d objects (c) Parallel axes theorem is applicable for 1d, 2d, 3d objects, but I axes theorem is not applicable for 3d objects. (d) For parallel axes theorem to be applicable one of the two parallel axes must pass through COM? covers all topics & solutions for Physics 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Which one of the following statements is correct (a) Parallel and axes theorem are valid for homogeneous as well as non-homogeneous objects (b) 1 axes theorem is applicable for 2d objects but not for 1d objects (c) Parallel axes theorem is applicable for 1d, 2d, 3d objects, but I axes theorem is not applicable for 3d objects. (d) For parallel axes theorem to be applicable one of the two parallel axes must pass through COM?.
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