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

A thin wire of length L and uniform linear mass density `rho` is bent

1.	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. `(rhoL^3)/(8pi^2)`B. `rhoL^3)/(16pi^2)`C. `(5rhoL^3)/(16pi^2)D. `(3rhoL^3)/(8pi^2)`
Answer» Correct Answer - D (d) Moment of inertia about the diameter of the circular loop (ring) `= (1)/)2) MR^2` Using parallel axis theorem 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 = Lrho and R = (L)/(2pi),` `:.I_(XX) = (3)/(2)(Lrho)((L)/(2pi))^2 = (3L^3rho)/(8pi^2)`

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

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