A rod of linear mass density 'λ' and length 'L' is bent to form a ring of radius 'R'.

Question

A rod of linear mass density \('\lambda'\) and length 'L' is bent to form a ring of radius 'R'. Moment of inertia of ring about any of its diameter is :

(1) \(\frac{\lambda L^3}{16\pi ^2}\)

(2) \(\frac{\lambda l^3}{12}\)

(3) \(\frac{\lambda L^3}{4\pi ^2}\)

(4) \(\frac{\lambda L^3}{8\pi ^2}\)

Answer 1

Correct option is : (4) \(\frac{\lambda L^3}{8\pi ^2}\) 

\(L = 2\pi R\)

\(I = \frac{MR^2}{2} = \frac{\lambda \times L }{2} \times \left(\frac{L}{2\pi}\right)^2 = \frac{\lambda L^3}{8\pi ^2}\)