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Question

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


A

2r

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B

r2

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C

2r

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D

r2

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Solution

The correct option is B

r2


The moment of inertia about the center and to the plane of the disc of radius r and mass m is

= 12mr2.

According to the question the radius of gyration of the disc about the required point = radius of the disc.

Therefore mk2 = 12mr2 + md2

(K = radius of gyration about acceleration point, d = distance of that point from the centre)

k2 = r22+d2

r2 = r22+d2 (K = r)

r22=d2 d = r2


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