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 :
.

Options

A. `(pL^(3))/(8pi^(2))`
B. `(pL^(3))/(16pi^(2))`
C. `(5pL^(3))/(16pi^(2))`
D. `(3pL^(3))/(8pi^(2))`

Explanation

Mass per unit length of the wirt =p Mass of L length, `M=pL` and since the wire of length L is bent in a form of circular loop therefore `2piR=LrArrRL//2pi` Moment of inertia of loop about given axis
`=(3)/(2)MR^(2)=(3)/(2)pL((L)/(2pi))^(2)=(3pL^(2))/(8pi^(2))`