Match the bodies and their specified axes of rotation in List I with their corresponding radius of gyration…

Match the bodies and their specified axes of rotation in List I with their corresponding radius of gyration in List II.
  1. A-IV, B-I, C-III, D-II
  2. A-I, B-II, C-IV, D-III
  3. A-II, B-III, C-I, D-IV
  4. A-I, B-IV, C-II, D-III

Solution

$\text{Hollow hemisphere: } I = \frac{2}{3} MR^2 = Mk^2 \\ k = \frac{\sqrt{2}}{\sqrt{3}} R \\ \text{Rod: } I = \frac{1}{12} MR^2 = mk^2 ; \\ k = \frac{R}{\sqrt{12}} \\ \text{Solid sphere: } I = I_{COM} + MR^2 \\ = \frac{2}{5} MR^2 + MR^2 = \frac{7}{5} MR^2 \\ I = \frac{7}{5} MR^2 = Mk^2 ; \\ k = \frac{\sqrt{7}}{\sqrt{5}} R \\ \text{Hollow cylinder: } I = MR^2 = Mk^2 \\ k = R$

Asked in: Aicharya Test Series 22.5.26

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