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A thin rod of length 4l and mass 4m is b...

A thin rod of length `4l` and mass `4m` is bent at the points as shown in Fig.
What is the moment of inertia of the rod about the axis passing through point `O` and perpendicular to the plane of the paper.

A

`(MI^(2))/3`

B

`(10 MI^(2))/3`

C

`(MI^(2))/(12)`

D

`(MI^(2))/(24)`

Text Solution

Verified by Experts

The correct Answer is:
B
Total `MI = I_(1) + I_(2) + I_(3) + I_(4)`
`I=2I_(1) + 2I_(2) , I= 2(I_(1) + I_(2))[I_(1) =I_(2), I_(2)=I_(4)]`
Now, `I_(2)=I_(3) = (MI^(3))/3`
Using parallel axis theorem, we have
`I = I_(cm) + Mx^(2)` and `x. sqrt(I^(2) + (1/2)^(2)), I_(1) = I_(4) =(Mr^(2))/12 + M [sqrt(r^(2) + (1/2)^(2))]^(2)`
Putting all values, we get `I = (10 MI^(2))/3`
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