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

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NDA (Held On: 17 Nov 2019) General Ability Test Previous Year paper

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Answer 1

CONCEPT:

Moment of inertia:

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 the 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:

Moment of inertia of the disc about an axis passing through center and perpendicular to its plane is given by -

Moment of inertia of the solid sphere about an axis passing through center and perpendicular to its plane is given by -

So, from above it is very clear that the moment of inertia of the disc is greater than the moment of inertia of the solid sphere.

Body	Axis of Rotation	Moment of inertia
Uniform circular ring of radius R	perpendicular to its plane and through the center	MR2
Uniform circular ring of radius R	diameter
Uniform circular disc of radius R	perpendicular to its plane and through the center
Uniform circular disc of radius R	diameter
A hollow cylinder of radius R	Axis of cylinder	MR2