question_answer

Four particles each of mass m are placed at the comers of a square of side length\[\ell \]. The radius of gyration of the system about an axis perpendicular to the square and passing through its centre is-

A) \[\frac{\ell }{\sqrt{2}}\]                          

B) \[\ell \]

C) \[\frac{\ell }{2}\]                                   

D) \[(\sqrt{2})\,\ell \]

Correct Answer: A

Solution :

Moment of inertia of system about point \[p\,\,=\,\,4m{{\left[ \frac{1}{\sqrt{2}} \right]}^{2}}\,\,=\,\,2m{{\ell }^{2}}\,\,and\,\,4\,m{{k}^{2}}\,\,=\,\,2m{{\ell }^{\text{2}}}\] \[\therefore \,\,k=\frac{\ell }{\sqrt{2}}\]