Question 561: Centre of Mass and Rotational Motion

Question

Radius of gyration of a thin uniform circular disc about the axis passing through its centre and perpendicular to its plane is $$\mathrm{K}_{\mathrm{c}}$$. Radius of gyration of the same disc about a diameter of the disc is $$K_d$$. The ratio $$K_c: K_d$$ is

Accepted Answer

Let the radius of the disc be $$R$$
$$\begin{aligned}
& 	herefore  \quad \mathrm{K}_{\mathrm{c}}=\frac{\mathrm{R}}{\sqrt{2}} \
& 	herefore  \quad\mathrm{K}_{\mathrm{d}}=\frac{\mathrm{R}}{2}
\end{aligned}$$
Taking the ratio,
$$	herefore \quad \frac{\mathrm{K}_{\mathrm{c}}}{\mathrm{K}_{\mathrm{d}}}=\frac{\frac{\mathrm{R}}{\sqrt{2}}}{\frac{\mathrm{R}}{2}}=\frac{\sqrt{2}}{1}$$

Answer

$$\sqrt{2}: 1$$

Answer

$$1: \sqrt{2}$$

Answer

$$2: 1$$

Answer

$$1: 4$$

Centre of Mass and Rotational Motion

Radius of gyration of a thin uniform circular disc about the axis passing through its centre and perpendicular to its plane is $\mathrm{K}_{\mathrm{c}}. Radius of gyration of the same disc about a diameter of the disc is K_d. The ratio K_c: K_d$ is

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