A solid sphere of mass and radius is modified in three different ways
PHYSICS · Subjective · CBSE · Physics · System of Particles and Rotational Motion · System of Particles and Rotational Motion
Problem
A solid sphere of mass M and radius R is modified in three different ways, the total mass remaining M in every case.
Modification A : the sphere is compressed uniformly so that its radius becomes 2R.
Modification B : the sphere is reshaped into a thin spherical shell of radius R.
Modification C : a concentric spherical cavity of radius 2R is bored out, leaving a thick spherical shell of outer radius R.
(i) For each modified body, state qualitatively whether its moment of inertia about a diameter is less than, equal to, or greater than that of the original solid sphere.
(ii) Arrange the original sphere and the three modified bodies in ascending order of moment of inertia about a diameter, giving clear reasons for your ranking based on mass distribution and radius of gyration.