Question

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

Answer 1

Answer:

The axis is at a distance 'd' = √(3/5) R from the center of the sphere

Please check the attached pic for the solution

Answer 2

The distance of the axis from the centre of the sphere is √(3/5)r .

Radius of gyration of a solid sphere of radius r about a certain axis is r.

moment of inertia of solid sphere about an axis passing through centre of it, I = 2/5 mr²

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

so, mk² = I + mx² , where k is radius of gyration.

⇒mr² = 2/5 mr² + mx²

⇒ 3/5 mr² = mx²

⇒x = √(3/5)r

hence, The distance of the axis from the centre of the sphere is √(3/5)r

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