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

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))=sqrt6=2.449` cm.