The figure shows a uniform rod lying along the x-axis. The locus of all the points lying on the xy-plane, about which the moment of inertia of the rod is same as that about O is:-

Question

G1 Physics · Accepted Answer

Let the rod's centre of mass be C. By the parallel-axis theorem, the moment of inertia about any point P is I at P = I at C + Md², where d=CP. For the moment of inertia at P to equal that about fixed point O, d must equal CO. Therefore P lies on a circle centred at C. Hence option B.