Two particles A and B of masses m and 2m are at a separation d. PQ is a line perpendicular to the line AB. Then minimum possible moment of inertia about PQ is

IPQ  will be minimum when line PQ passes through the centre of mass of the system∴ AP = 2m×d3m = 2d3      and  BP = d−2d3 = d3 ∴IPQ min=m2d32+2md32a                                      =23md2