A thin wire of length L and uniform linear mass density - is bent into a circular loop with center O as shown- The moment of inertia of the loop about the axis XX- is

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Rotational Inertia

A thin wire o...

Question

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

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Solution

The correct option is D

A thin wire of length 'L' is bent into circular loop

$∴$ Circumference of circular loop $= 2 π R = L$

= $R = \frac{L}{2 π}$

Moment of inertia of loop about its natural axis passing through 'O'

$I_{0} = M R^{2}$

Moment of inertia about

$Y Y^{'} = I^{'} = \frac{M R^{2}}{2}$

By applying parallel axes theorem $I = I^{'} + M R^{2}$

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

The correct option is D A thin wire of length 'L' is bent into circular loop ∴ Circumference of circular loop =2πR=L = R=L2π Moment of inertia of loop about its natural axis passing through 'O' I0=MR2 Moment of inertia about YY′=I′=MR22 By applying parallel axes theorem I=I′+MR2