Question

find the expression for radius of gyration of a solid sphere about one of its diameter.

Answer 1

first of all , you should understand that what is radius of gyration. Radius is defined as the distance from the axis of rotation to a point where the total mass of the body is supposed to be concentrated, so that the moment of inertia about the axis may remain the same.

we know, moment of inertia of sphere about an axis passing through one of its diameter is given by, $I=\frac{2}{5}mr^2$

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

now, k is radius of gyration then,
$\frac{2}{5}mr^2=mk^2$

so, $k=\sqrt{\frac{2}{5}}r$ is the radius of gyration.

Answer 2

Answer:

√0.4R

Explanation: