Radius of gyration of a thin uniform circular disc about the axis passing through its centre and perpendicular to its plane is K c . Radius of gyration of the same disc about a diamter of the disc i

Question

Radius of gyration of a thin uniform circular disc about the axis passing through its centre and perpendicular to its plane is K c ​ . Radius of gyration of the same disc about a diamter of the disc is K d ​ . the ratio K d ​ : K c ​ is

TestHub · Accepted Answer

Moment of inertia of a uniform circular disc about an axis passing through its centre and perpendicular to its plane is $I_{c} = \frac{1}{2} M R^{2}$ .

Radius of gyration $K_{c} = \frac{I _{c}}{M} = \frac{R}{2}$ .

Moment of inertia of the disc about its diameter is $I_{d} = \frac{1}{4} M R^{2}$ .

Radius of gyration $K_{d} = \frac{I _{d}}{M} = \frac{R}{2}$ .

Ratio $\frac{K _{d}}{K _{c}} = \frac{\frac{R}{2}}{\frac{R}{2}} = \frac{1}{2}$ .

Thus, $K_{d} : K_{c} = 1 : 2$ .

Answer: $1 : 2$

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