Medium
What is the radius of gyration? Write its unit and dimensional formula.
(N/A) The radius of gyration of a body about a given axis is defined as the distance from the axis of rotation to a point where,if the entire mass of the body were concentrated,its moment of inertia would be the same as the actual body.
Mathematically,$I = MK^2$,where $I$ is the moment of inertia,$M$ is the total mass,and $K$ is the radius of gyration.
Thus,$K = \sqrt{I/M}$.
Unit: The $SI$ unit of the radius of gyration is the meter $(m)$.
Dimensional formula: Since it represents a distance,its dimensional formula is $[M^0 L^1 T^0]$.
Mathematically,$I = MK^2$,where $I$ is the moment of inertia,$M$ is the total mass,and $K$ is the radius of gyration.
Thus,$K = \sqrt{I/M}$.
Unit: The $SI$ unit of the radius of gyration is the meter $(m)$.
Dimensional formula: Since it represents a distance,its dimensional formula is $[M^0 L^1 T^0]$.
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The moment of inertia $(M.I.)$ of four bodies,having the same mass $M$ and radius $R$,are reported as follows:
$I_{1} = M.I.$ of a thin circular ring about its diameter.
$I_{2} = M.I.$ of a circular disc about an axis perpendicular to the disc and passing through the centre.
$I_{3} = M.I.$ of a solid cylinder about its axis.
$I_{4} = M.I.$ of a solid sphere about its diameter.
Then:
$I_{1} = M.I.$ of a thin circular ring about its diameter.
$I_{2} = M.I.$ of a circular disc about an axis perpendicular to the disc and passing through the centre.
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Then:
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