Four identical thin rods of mass m and length l form a square frame as shown in fig. Find the MOI of the frame about an axis passing through one of its corner and perpendicular to its plane.
A
10ml23
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B
43ml23
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C
25ml2
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D
ml23
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Solution
The correct option is A10ml23
Using parallel axis theorem
M.O.I (I) of individual rod about I0= M.O.I of individual rod about it's C.O.M+md2 I=ml212+m(l2)2=ml23
Now considering all four rod as system C.O.M of system will be at O. ∴Icom=4×I=4ml23
Using parallel axis theorem, Iz=Icom+(4m)d2
Here d=AC2=l√22 Iz=Icom+(4m)(l√22)2=4ml23+4ml22=10ml23