Question

The radius of gyration of a hollow sphere of radius r, about a certain axis is r. The distance of this axis from the centre of sphere is

√61/19r

√12r

√5r

√r/√3

Answer 1

Given info : The radius of gyration of a hollow sphere of radius r, and a certain axis is r.

To find : the distance of this axis from the centre of sphere is ....

solution : moment of inertia of a hollow sphere with respect of centre of mass is given by, I = 2/3 mr²

where r is radius of hollow sphere and m is mass.

let the distance of the axis from centre of sphere is h.

radius of gyration is r.

so, I = mk² = mr² [radius of gyration, k = r ]

using parallel axis theorem,

I = I_cm + mh²

⇒mr² = 2/3 mr² + mh²

⇒1/3 mr² = mh²

⇒h = 1/√3 r

Therefore the distance of axis from the centre of sphere is r/√3 .