A rod of linear mass density ' 
' and length ' 
' is bent to form a ring of radius ' R '. Moment of inertia of ring about any of its diameter is.
Text Solution
Verified by ExpertsA
First, relate the length of the rod to the circumference of the ring:
The mass of the ring, denoted by 
, is the product of the linear mass density and the length of the rod:
The moment of inertia of a ring about a diameter is given by the formula:
Substituting the expression for mass 
and using the relation for 
derived from the circumference:
Simplifying the expression, we arrive at:
This is the moment of inertia of the ring about any of its diameters.
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