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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

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

B

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

C

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

D

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

Text Solution

Verified by Experts

The correct Answer is:
D
The moment of inertia of the loop about `XX'` axis is `I_(XX) = (mR^(2))/2 + mR^(2) = 3/2 mR^(2)`
where, m = mass of the loop and R = radius of the loop
Here, `m=L rho` and `R = L/(2pi)`, therefore, `I_(XX') = 3/2(Lrho)(L/(2pi))^(2) =(3L^(2)rho)/(8pi^(2))`
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