A thin wire of length (l ) having a linear density ( ) is bent into a circular loop with (C ) as its centre as shown in the figure. The moment of inertia of the loop about the line (A B ) is

Step-by-step solution

Given, length of a thin wire (=l ) Linear density of the wire (= ) Let the mass of the wire (=M ) Now, according to the question Here, circular loop of the wire with centre, C. (R ) is the radius of circular loop of wire. ( ) Moment of inertia axis passing through the centre and perpendicular to the plane (A B ). (I_ A B =M R^2 )...(i) ( ) Moment of inertia axis passing through the centre of circular loop about its diameter , (I_ CM = 1 2 M R^2 )...(ii) Now, the total moment of inertia for circular loop of wire. If