Question 593: Centre of Mass and Rotational Motion

Question

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

Accepted Answer

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

Answer

$$1:\sqrt2$$

Answer

$$2:1$$

Answer

$$\sqrt2:1$$

Answer

$$3:2$$

Centre of Mass and Rotational Motion

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

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