System Of Particles And Rotational Motion Ques 58

58. 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

[NEET Kar. 2013, 2008]

(a) $\sqrt{2}: 1$

(b) $1: \sqrt{2}$

(c) $3: 2$

(d) $2: 1$

Show Answer

Answer:

Correct Answer: 58.(a)

Solution:

  1. (a) $\because I=M K^{2} \therefore K=\sqrt{\frac{I}{M}}$

$I _{\text{ring }}=M R^{2}$ and $I _{\text{disc }}=\frac{1}{2} M R^{2}$

$\frac{K_1}{K_2}=\sqrt{\frac{I_1}{I_2}}=\sqrt{\frac{M R^{2}}{(\frac{M R^{2}}{2})}}=\sqrt{2}: 1$

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