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

Options

A. an ellipse
B. a circle
C. a parabola
D. a striaght line

Answer

B

Explanation

Let us take any point `P` on `x-y` plane. The `MI` of the rod about `O` is
`I_(P)=I_(CM)+Mr^(2)`

Hence `I_(P)=(ML^(2))/12+M[(x-L/2)^(2)+y^(2)]`
MI of the rod abut `O, I_(0)=(ML^(2))/3`
Applying `I_(P)=I_(0)`, we get an equation of a circle .