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  • The ratio of the radius of gyration of a thin uniform disc about an axis passing through its centre and normal to its plane to the radius of gyration of the disc about its diameter is :<div cla

The ratio of the radius of gyration of a thin uniform disc about an axis passing through its centre and normal to its plane to the radius of gyration of the disc about its diameter is :

Option: 1

\sqrt{2}:1


Option: 2

4:1


Option: 3

1:\sqrt{2}


Option: 4

2:1


Answers (1)

best_answer

Let the moment of inertia of a thim uniform disc about an axis normal to its plane and about its diameter be \mathrm{I}_{1} & \mathrm{I}_{2} respectively

\begin{aligned} &\mathrm{I}_{1}=\frac{\mathrm{M R}^{2}}{2}=\mathrm{M K}_{1}^{2} \\ &\mathrm{I}_{2}=\frac{\mathrm{M R}^{2}}{4}=\mathrm{M K}_{2}^{2} \\ &\frac{\mathrm{K}_{1}}{\mathrm{K}_{2}}=\sqrt{2} \end{aligned}
The correct option is (1)

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Nehul

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