Match List-I with List-II.
**List-I**
(a) MI of the rod (length $L$, mass $M$) about an axis $\perp$ to the rod passing through the midpoint
(b) MI of the rod (length $L$, mass $2M$) about an axis $\perp$ to the rod passing through one of its ends
(c) MI of the rod (length $2L$, mass $M$) about an axis $\perp$ to the rod passing through its midpoint
(d) MI of the rod (length $2L$, mass $2M$) about an axis $\perp$ to the rod passing through one of its ends
**List-II**
(i) $\dfrac{8ML^2}{3}$
(ii) $\dfrac{ML^2}{3}$
(iii) $\dfrac{ML^2}{12}$
(iv) $\dfrac{2ML^2}{3}$
Choose the correct answer from the options given below:
Answer: (C) (a)–(iii), (b)–(iv), (c)–(ii), (d)–(i)
Use $I_{\text{centre}} = \dfrac{m\ell^2}{12}$ and $I_{\text{end}} = \dfrac{m\ell^2}{3}$.
(a) $\dfrac{ML^2}{12}$ → (iii)
(b) $\dfrac{2M L^2}{3}$ → (iv)
(c) $\dfrac{M(2L)^2}{12} = \dfrac{ML^2}{3}$ → (ii)
(d) $\dfrac{2M(2L)^2}{3} = \dfrac{8ML^2}{3}$ → (i)
Solution by Sreeraj P, M.Sc Physics