calculate radius of hydration of a cylindrical Rod of mass 'm'and length 'l'about an axis of rotation perpendicular to its length and passing through the center.
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Radius of gyration of a body about a given axis is the perpendicular distance of a point from the axis, where if whole mass of the body were concentrated, then the body shall have the same moment of inertia as it has with the actual distribution of mass. This distance is represented by K. The momentum of inertia of a body of mass M and radius of gyration K is given by,
I = MK2
We know moment of inertia of a cylindrical thin rod of mass ‘m’ and length ‘L’ about an axis passing through its midpoint and perpendicular to it is = (1/12)mr2
= m(r2/12)
So, by definition,
K2 = r2/12
=> K = r/(2√3)
This is the radius of gyration.
I = MK2
We know moment of inertia of a cylindrical thin rod of mass ‘m’ and length ‘L’ about an axis passing through its midpoint and perpendicular to it is = (1/12)mr2
= m(r2/12)
So, by definition,
K2 = r2/12
=> K = r/(2√3)
This is the radius of gyration.
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