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.

Answer 1

The moment of inertia about the center and ⊥ to the plane of the disc of
radius r and mass m is = mr².
According to the question the radius of gyration of the disc about a point = radius of the disc.
Therefore mk² = ½ mr² + md²
(K = radius of gyration about acceleration point, d = distance of that point from the centre)
 K² = r²/2 + d²
 r² = r²/2 + d² (K = r)
 r²/2 = d² = d = r / √2 .