Question

Two point masses M and 3M are placed at a distance r. The moment of inertia of the system about an Axis passing through the centre of mass of system and perpendicular to the line joining the points masses is

Answer 1

Center of mass will be toward 3M and than M due to their difference.

Distance from center of mass by m = x

distance from center of mass by 3M = r-x

so,

Mx = 3M (r-x)

Mx= 3Mr - 3Mx

x= 3r/4  

and 

r-x= r/4

Center of mass of the system= 3M(r-x)² + Mx² 

=(3Mr²/16)+(M9r²/16)  

= 3/4 Mr²