Q105 / 200 · NEET 2004 · Physics

The ratio of the radii of gyration of a circular disc about a tangential axis in the plane of the disc and of a circular ring of the same radius about a tangential axis in the plane of the ring is:

  • A
    $2: 3$
  • B
    $2: 1$
  • Correct answer
    C
    $\sqrt{5}: \sqrt{6}$
  • D
    $1: \sqrt{2}$

Solution

The radius of gyration of disc about a tangential axis in the plane of disc is $k_1$ $$ \therefore \quad k_1=\frac{\sqrt{5}}{2} R $$ And radius of gyration of circular ring of same radius about tangential axis is given by: $$ \begin{aligned} k_2 & =\frac{\sqrt{3}}{2} \mathrm{R} \\ \therefore \quad \frac{k_1}{k_2} & =\frac{\sqrt{5}}{2} R \times \frac{\sqrt{2}}{\sqrt{3} R} \\ & =\frac{\sqrt{5}}{\sqrt{6}} \end{aligned} $$

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

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