Four particles each of the mass m are placed at the corners of a square of side length l . The radius of gyration of the system about an axis perpendicular to the square and passing through its centre is

Step-by-step solution

The given situation is shown in figure. Moment of inertia of the systems about an axis perpendicular to the square and passing through the centre is given as aligned I &=m ( l 2 )²+m ( l 2 )²+m ( l 2 )²+m ( l 2 )² &=4 m l² 2 =2 m l² aligned If k be the radius of gyration, then I=4 m k² From Eegs. (i) und (ii), we have aligned 2 m l² &=4 m k² k &= 1 2 aligned