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Four thin rods of same mass M and same l...

Four thin rods of same mass M and same length l, form a square as shown in figure. Moment of inertia of this system about an axis through centre O and perpendicular to its plane is

A

`(4)/(3)Ml^(2)`

B

`(Ml^(2))/(3)`

C

`(Ml^(2))/(6)`

D

`(2)/(3)Ml^(2)`

Text Solution

Verified by Experts

The correct Answer is:
A
Moment of inertia of rod AB about point `P=(1)/(12)Ml^(2)`
M.I. of rod AB about point `O=(Ml^(2))/(12)+M((l)/(2))^(2)=(1)/(3)Ml^(2)` [by the theorem of parallel axis]
and the system consists of 4 rods of similar type so by the symmetry `I_("System")=(4)/(3)Ml^(2)`.
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