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The radius of gyration of a uniform rod of length L about on axis passing through its centre of mass is
- a)L/√12
- b)L2/12
- c)L/√3
- d)L/√2
Correct answer is option 'A'. Can you explain this answer?
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The radius of gyration of a uniform rod of length L about on axis pass...
The radius of gyration of an uniform rod of length L about an axis passing through its centre of mass and perpendicular to its length is. Solution : (a) K=√IM=√ML2/12M=L√12.
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The radius of gyration of a uniform rod of length L about on axis pass...
The correct answer is:
The radius of gyration of a uniform rod of length L about an axis passing through its center of mass is given by:
\[k = \frac{L}{\sqrt{12}}\]
This formula is derived from the moment of inertia of a uniform rod about an axis passing through its center of mass, which is given by:
\[I = \frac{1}{12}mL^2\]
where m is the mass of the rod. The radius of gyration is defined as the distance from the axis of rotation at which the entire mass of the rod could be concentrated to produce the same moment of inertia. In this case, the radius of gyration is given by:
\[k = \sqrt{\frac{I}{m}} = \sqrt{\frac{\frac{1}{12}mL^2}{m}} = \sqrt{\frac{L^2}{12}} = \frac{L}{\sqrt{12}}\]
Therefore, the radius of gyration of a uniform rod of length L about an axis passing through its center of mass is L/√12.
The radius of gyration of a uniform rod of length L about an axis passing through its center of mass is given by:
\[k = \frac{L}{\sqrt{12}}\]
This formula is derived from the moment of inertia of a uniform rod about an axis passing through its center of mass, which is given by:
\[I = \frac{1}{12}mL^2\]
where m is the mass of the rod. The radius of gyration is defined as the distance from the axis of rotation at which the entire mass of the rod could be concentrated to produce the same moment of inertia. In this case, the radius of gyration is given by:
\[k = \sqrt{\frac{I}{m}} = \sqrt{\frac{\frac{1}{12}mL^2}{m}} = \sqrt{\frac{L^2}{12}} = \frac{L}{\sqrt{12}}\]
Therefore, the radius of gyration of a uniform rod of length L about an axis passing through its center of mass is L/√12.
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The radius of gyration of a uniform rod of length L about on axis passing through its centre of mass isa)L/√12b)L2/12c)L/√3d)L/√2Correct answer is option 'A'. Can you explain this answer?
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