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

Three particles of masses 1g, 2g and 3g are at distances of 1 cm, 2 cm

1.	Three particles of masses 1g, 2g and 3g are at distances of 1 cm, 2 cm and 3 cm from the axis of rotation. Find (i) the moment of inertia of the system and (ii) the radius of gyration of the system.
Answer» SOLUTION :(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=36g cm^(2)` (ii) The radius of gyration, `K=sqrt((I)/("Total mass"))=sqrt((36)/(1+2+3))=sqrt(6)=2.449 cm`.