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A thin wire of length 'L' and linear mass density 'm' is bent into a circular ring (in x-y plane) with centre 'C' as shown in figure. The moment of inertia of the ring about an axis yy' will be :

Asked in NEET 2026 · Standard bodies and axis theorems

• (1) (3mL²)/(8π)
• (2) (3mL²)/(8π²)
• (3) (3mL³)/(8π)
• (4) (3mL³)/(8π²)

Step-by-step solution

Why the other options are wrong

• (1) Two slips: treats m as the mass of the ring (it is mass per unit length, so the mass is mL), and squares the 2 but not the π in r=L/(2π).
• (2) Treats m as the mass of the ring; it is mass per unit length, so the mass is mL and the answer carries L³.
• (3) Squares the 2 but not the π in r=L/(2π): r²=(L²)/(4π²), not (L²)/(4π).

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