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Three rings each of mass m and radius R are so placed that they touch each other. The radius of gyrations of the system about the axis as shown in fig.

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Asked by m.nilu 19th October 2018, 12:55 AM
Answered by Expert
Answer:
Moment of inertia of ring-1 with respect to the given axis = begin mathsize 12px style m cross times r squared over 2 end style.............(1)
where m is mass of ring and r is its radius.
 
Moment of inertia of ring-2 with respect to the given axis, by parallel axis theorem  = begin mathsize 12px style m cross times r squared over 2 space plus space m cross times r squared space equals 3 over 2 space m cross times r squared end style .....................(2)
 
similarly Moment of inertia of ring-3 with respect to the given axis, by parallel axis theorem  =   begin mathsize 12px style 3 over 2 space m cross times r squared end style.....................(3)
 
Moment of inertia I of the system of combined rings is given by, I = begin mathsize 12px style open parentheses 3 over 2 space plus space 3 over 2 space plus 1 half close parentheses space m cross times r squared space equals 7 over 2 space m cross times r squared end style
 
Since combined mass of the system is 3m, radius of gyration =[ I/(3m) ]1/2  begin mathsize 12px style square root of 7 over 6 end root space r end style
Answered by Expert 19th October 2018, 4:43 AM
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