A solid sphere and a hollow sphere have the same mass and same radius. Which one has the higher moment of inertia about its diameter?

CONCEPT:

Moment of inertia:

• The moment of inertia of a rigid body about a fixed axis is defined as the sum of the product of the masses of the particles constituting the body and the square of their respective distances from the axis of rotation.
• The moment of inertia of a particle  is

I = mr2

Where r = the perpendicular distance of the particle from the rotational axis.

• Moment of inertia of a body made up of a number of particles (discrete distribution)

I = m1r12 + m2r22 + m3r32 + m4r42 + -------

EXPLANATION:

• The moment of inertia of a solid sphere of mass 'M' and radius 'R' about its diameter is 

\(⇒ I_s =\frac{2}{5}MR^2=0.4MR^2\)    ----- (1)

• The moment of inertia of a hollow sphere of mass 'M' and radius 'R2' about its diameter is 

\(⇒ I_h =\frac{2}{3}MR^2=0.67MR^2\)     ----- (2)

• From the above two-equation, it is clear that the moment of inertia of a hollow sphere is more than that of a hollow sphere. Therefore option 4 is correct.