Three particles of masses `1g, 2g`and `3g` are at distances of `1cm, 2cm` and `3cm` from the axis of rotation. Find i) the moment of inertia of the system and ii) the radius of gyration of the system.

Explanation

(i) The MI of the system , `I=m_(1)r_(1)^(2)+m_(2)r_(2)^(2)+m_(3)r_(3)^(2)`
`=1xx1^(2)+2xx2^(2)+3xx3^(2)=1+8+27=36gcm^(2) `
(ii) The radius of gyration
`k=sqrt((I)/("Total mass"))=sqrt((36)/(1+2+3))=sqrt(6)=2.449cm`