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. `(rho L^3)/(8 pi^2)`
B. `(rho L^3)/(16 pi^2)`
C. `(5 rho L^3)/(8 pi^2)`
D. `(3 rho L^3)/(8 pi^2)`

Answer

D

Explanation

(d) `L = 2 pi r rArr r = (L)/(2 pi), m = rho L`
`I_(xy) = (3)/(2) mr^2`
=`(3)/(2) rho L ((L)/(2 pi))^2 = (3)/(8) (rho L^3)/(8 pi^2)`
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