Find the radius of gyration of a system of particles about an axis passing through the center of mass and perpendicular to the line joining the particles. The system consists of two particles of masses `m_(1)` and `m_(2)` placed at separation at `r`

Explanation

`x_(c.m.)=(m_(1)xx0+m_(2)r)/(m_(1)+m_(2))=(m_(2)r)/(m_(1)+m_(2))`
`I_(A)=m_(1)x_(c.m.)^(2)+m_(2)(r-x_(c.m.))^(2)`
`= (m_(1)m_(2))/(m_(1)+m_(2))r^(2)=(m_(1)+m_(2))k^(2)`
`k=(sqrt(m_(1)m_(2)))/(m_(1)+m_(2))r`