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A thin wire of length L and uniform line...

A thin wire of length `L` and uniform linear mass density `rho` is bent into a circular loop with centre at `O` as shown. The moment of inertia of the loop about the axis `XX'` is :
.

A

`rho L^(3)//8 pi^(2)`

B

`rho L^(3)//16 pi^(2)`

C

`5 rho L^(3)//16 pi^(2)`

D

`3 rho L^(3)//8 pi^(2)`.

Text Solution

Verified by Experts

The correct Answer is:
D
From parallel axis theorem
`I_(xx') = I_(0) + MR^(2) rArr I_(xx') = (1)/(2) MR^(2) + MR^(2)`
`I_(xx') = (3)/(2) MR^(2)`
`I_(xx') = (3)/(2) rho xx L xx ((L)/(2 pi))^(2) rArr I_(xx') = (3)/(8) (rho L^(3))/(8 pi^(2))`.
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