Question

which one will have a greater value of moment inertia a) a ring of radius 1kg of radius 2m. b) a disc of mass 2kg of radius 2m. c) a solid sphere of mass 5kg and radius 2m.​

Answer 1

A] Ring :

Moment of inertia of a ring about an axis passing through its centre and perpendicular to plane the plane of ring given by I = MR²

➛ I = MR²

➛ I = 1 × 2²

➛ I = 1 × 4

➛ I = 4 kg m²

B] Disc :

Moment of inertia of a disc about an axis passing through its centre and perpendicular to the plane of disc is given by I = MR²/2

➛ I = MR²/2

➛ I = 2 × 2² / 2

➛ I = 2 × 2

➛ I = 4 kg m²

C] Solid sphere :

Moment of inertia of a solid sphere about an axis passing through its centre is given by I = 2MR²/5

➛ I = 2MR²/5

➛ I = 2 × 5 × 2² / 5

➛ I = 2 × 4

➛ I = 8 kg m²

____________________________

$\bigstar\:\underline{\boxed{\bf{\orange{I_{Sphere}>I_{Ring}=I_{Disc}}}}}$

Answer 2

$\huge{\boxed{\bold{Question}}}$

which one will have a greater value of moment inertia a) a ring of radius 1kg of radius 2m. b) a disc of mass 2kg of radius 2m. c) a solid sphere of mass 5kg and radius 2m.

A] Ring :

Moment of inertia of a ring about an axis passing through its centre and perpendicular to plane the plane of ring given by I = MR²

➛ I = MR²

➛ I = 1 × 2²

➛ I = 1 × 4

➛ I = 4 kg m²

B] Disc :

Moment of inertia of a disc about an axis passing through its centre and perpendicular to the plane of disc is given by I = MR²/2

➛ I = MR²/2

➛ I = 2 × 2² / 2

➛ I = 2 × 2

➛ I = 4 kg m²

C] Solid sphere :

Moment of inertia of a solid sphere about an axis passing through its centre is given by I = 2MR²/5

➛ I = 2MR²/5

➛ I = 2 × 5 × 2² / 5

➛ I = 2 × 4

➛ I = 8 kg m²

I Spher>I Ring

=I Disc