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

Answer

B

Explanation

The moment of inertia about the centre and perpendicular to the plane of the disc of radius and mas m is `=mr^2`
According to the question the radius of gyration of the disc about a about =radius of the disc.
Therefoe `mk^2=1/2mr^2+md^2`
(k=radius of gyration about accelertion point, d=distance of that point from the centre)
`rarr K^2=r^2/2+d^2`
`rarr r^2=r^2/2+d^2`
`rarr r^2/2=d^2`
`rarr d=r/sqrt2`