Q125 / 150 · MHT CET 2024 (03 May Shift 1) · Physics

Ratio of radius of gyration of a circular dise to that of circular ring each of same mass and radius around their respective axes is

  • A
    $\sqrt{2}: 1$
  • B
    $\sqrt{2}: \sqrt{3}$
  • C
    $\sqrt{3}: \sqrt{2}$
  • Correct answer
    D
    $1: \sqrt{2}$

Solution

Let $I_d$ and $I_r$ be the respective M.I. of the disc and the ring. If $\mathrm{K}_{\mathrm{d}}$ and $\mathrm{K}_{\mathrm{r}}$ are the respective radii of gyration, $\begin{array}{ll} & \mathrm{I}_{\mathrm{d}}=\frac{1}{2} \mathrm{MR}^2=\mathrm{MK}_{\mathrm{d}}^2 \\ \therefore \quad & \mathrm{~K}_{\mathrm{d}}=\frac{\mathrm{R}}{\sqrt{2}} \\ & \mathrm{I}_{\mathrm{r}}=\mathrm{MR}^2=\mathrm{MK}_{\mathrm{r}}^2 \\ \therefore \quad & \mathrm{~K}_{\mathrm{r}}=\mathrm{R} \\ \therefore \quad & \frac{\mathrm{~K}_{\mathrm{d}}}{\mathrm{~K}_{\mathrm{r}}}=\frac{\mathrm{R}}{\sqrt{2}}=\frac{1}{\sqrt{2}} \end{array}$

Hence, the correct answer is option: 'D'.

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