Question

AB and CD are two identical rods each of length l and mass m joined to form a cross. The
moment of inertia of the system about a bisector
of the angle between the rods (XY).
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Answer 1

Let moment of inertia of each rod be I

Rods CD and AB are perpendicular to each other. So moment of inertia about an axis passing through the centre and perpendicular to both AB and CD I', is 2I  = I'(according to perpendicular axes theorem)

Let the bisectors be X'Y' and XY.

XY + X'Y' = I'

XY = X'Y'

2XY = I'

XY = I'/2

XY = ML²/12