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Question

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 A 10ml23

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=l22
Iz=Icom+(4m)(l22)2 =4ml23+4ml22 =10ml23

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