Q101 / 150 · MHT CET 2021 (20 Sep Shift 1) · Physics

The ratio of radii of gyration of a circular ring and circular disc of the same mass and radius, about an axis passing through their centres and perpendicular to their planes is

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

Solution

$\mathrm{I}=\mathrm{MK}^2$ For a ring, $\mathrm{MR}^2=\mathrm{MK}_{\mathrm{r}}{ }^2 \quad \therefore \mathrm{K}_{\mathrm{r}}=\mathrm{R}$ For a disc, $\frac{\mathrm{MR}^2}{2}=\mathrm{MK}_{\mathrm{d}}^2 \quad \therefore \mathrm{K}_{\mathrm{d}}=\frac{\mathrm{R}}{\sqrt{2}}$ $$ \frac{\mathrm{K}_{\mathrm{r}}}{\mathrm{K}_{\mathrm{d}}}=\sqrt{2} $$

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

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