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Q.

The radius of gyration of a uniform disc about a line perpendicular to the disc is equal to its radius. Find the distance of the line from the centre of the disc.

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a

$d = \frac{R}{\sqrt{2}}$

b

$d = \frac{R}{\sqrt{7}}$

c

$d = \frac{R}{\sqrt{5}}$

d

$d = \frac{R}{\sqrt{3}}$

answer is A.

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Detailed Solution

detailed_solution_thumbnail

Radius of the disc = R

Radius of gyration=K

Question Image

$I = I_{G} + {Md}^{2}$

${MK}^{2} = \frac{{MR}^{2}}{2} + {Md}^{2} \Rightarrow K^{2} = \frac{R^{2}}{2} + d^{2}$

$R^{2} = \frac{R^{2}}{2} + d^{2} [∵ K = R] \frac{R^{2}}{2} = d^{2} \Rightarrow distance d = \frac{R}{\sqrt{2}}$

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