A thin uniform circular ring of mass M and radius R is in XY plane with its center coinciding with the origin. If it’s moment of inertia about Z-axis is same as its moment of inertia about the line y = x + c, the value of c is

moment of inertia about Z axis = MR2 moment of inertia about a diameter parallel to the line =MR22 y=x+c  slope of the line is 1 i.e, θ=450 perpendicular distance between the lines=c sin 450 applying parallel axis theorem MR2=MR22+M(c sin 450)2 solving c=R