System of Particles and Rotational Motion - Result Question 55
59. The ratio of radii of gyration of a circular ring and a circular disc, of the same mass and radius, about an axis passing through their centres and perpendicular to their planes are
(a) $\sqrt{2}: 1$
(b) $1: \sqrt{2}$
(c) $3: 2$
(d) $2: 1$
[NEET Kar. 2013, 2008]
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Answer:
Correct Answer: 59. (a)
Solution:
(a) $\because I=M K^{2} \therefore K=\sqrt{\frac{I}{M}}$
$I _{\text{ring }}=M R^{2}$ and $I _{\text{disc }}=\frac{1}{2} M R^{2}$
$\frac{K_1}{K_2}=\sqrt{\frac{I_1}{I_2}}=\sqrt{\frac{M R^{2}}{(\frac{M R^{2}}{2})}}=\sqrt{2}: 1$
