Question

find the radius of gyration of a rod of mass m and length 2l about an axis passing through one of its eneds and perpendicular to its length.

Answer 1

The radius of gyration of a rod of mass m and length 2l about an axis passing through one of its eneds and perpendicular to its length can be calcuated by:-

I= MK^2

where I = moment of inertia

M = mass

K= radius of gyration

So, first we have to find out moment of inertia which wil be-

13ml^2 /3

therefore, K= $\sqrt13mlx^{2} 2 / m$

                K= $l\sqrt 13$