Question

4. Four rods of mass M and length I are joined at the centre. Find the moment of inertia of the system about
axis of rotation AA' shown here.
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Answer 1

Answer:

From Perpendicular axis theorem 

Iz=Iy+Ix{Ix=Iy}

Iz=2Ix

from parallel axis theorem Iz=Icom+md2

⇒ Iz=12ML2+M(2L)2

⇒ Iz=12ML2+4ML2 ⇒Iz=31ML2→ For single Ros

for 4 rod Iz=4×31ML2=34ML2