question_answer

Calculate radius of gyration of a cylindrical rod of mass m and length L about an axis of rotation perpendicular to its length and passing through the centre.

Answer:

                K = ? mass = m, length L.                 Moment on inertia of the rod about an axis perpendicular to its length and passing through the centre is                 \[I=\frac{m{{L}^{2}}}{12}\] Also, \[I=m{{K}^{2}}\]                                    \[\therefore \]  \[m{{K}^{2}}=\frac{m{{L}^{2}}}{12}\]      or                 \[K=\frac{L}{\sqrt{12}}=\frac{L}{2\sqrt{3}}\]