A uniform thin circular ring of mass M and radius R is melted and recast into another ring of the same mass but of radius 2R. The density of the material remains unchanged.
a. (a) Write the expression for the moment of inertia of a ring of mass M and radius R about the axis perpendicular to its plane and passing through its centre.
b. (b) Calculate the moment of inertia of the new ring about a similar central axis.
c. (c) Determine the ratio IoldInew and comment on how doubling the radius affects the moment of inertia.